Methods of flash sintering

ABSTRACT

This disclosure provides methods of flash sintering and composition created by these methods.

RELATED APPLICATIONS

This application claims priority from U.S. Provisional Application No.61/513,246 filed on Jul. 29, 2011, incorporated by reference herein inits entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under grant numberDE-FG02-07ER46403 awarded by the U.S. Department of Energy. Thegovernment has certain rights in the invention.

FIELD

The present disclosure is directed to methods for producing sinteredceramic materials in very short times and at low temperatures ascompared to traditional methods.

BACKGROUND

Dense ceramic bodies are traditionally produced by sintering greenpowder compacts at high temperatures, in a process that is time andenergy intensive. For example, zirconia traditionally requires severalhours at 1400° C. Although electromagnetic and electrical field assistedsintering techniques (FAST) allow shorter times and temperatures, thereremains a need in the art for techniques that further reduce the energyrequirements and cost.

SUMMARY

Provided herein are methods of flash sintering.

In one aspect, provided herein is a method of sintering a material,comprising simultaneously exposing the material to heat and to a DC, ACor pulsed electrical field that is applied by a potential differenceacross the material, such that the material is sintered, wherein thetime between the onset of sintering and the completion of sintering isless than one minute.

In one embodiment of the method, the time between the onset of sinteringand the completion of sintering is less than 5 seconds.

In certain embodiments of the method, the electrical field is between7.5 V/cm and 1000 V/cm.

In another embodiment of the method, the onset of sintering isaccompanied by an increase in power dissipation within the material,wherein the power dissipation is manifested as an increase in thecurrent flowing through the material. In still another embodiment of themethod, the onset of sintering is accompanied by a sudden increase inpower dissipation within the material, wherein the power dissipation ismanifested as a sudden increase in the current flowing through thematerial. In certain embodiments of the method, the power dissipation isbetween 1 W and 100 W. In other embodiments, the range is typically from10 to 1000 mWmm⁻³.

In still another embodiment of the method, the onset of sintering isaccompanied by a non-linear increase in the conductivity of thematerial.

In other embodiments of the method, the electrical voltage is applied tothe material with two electrodes that are electronically conducting. Ina particular embodiment, the electrodes are made from a metal or from anelectronically conducting ceramic material. In some embodiments, theelectrodes are not physically in contact with the material.

In still another embodiment of the method, the electrical field is fixedand the heat is increased at a constant rate. In certain embodiments ofthe method, the heat is increased at a rate between 1° C. per minute to100° C. per minute.

In one embodiment of the method, the temperature of the furnacecontaining the material is fixed and the applied voltage field isincreased at a constant rate until the onset of sintering.

In still another embodiment of the method, the onset of sintering isaccompanied by an increase in the relative density of the material to80-100% of the theoretical density.

In a particular embodiment, the method comprises simultaneously exposingthe material to an electrical field and to heat, such that the materialis sintered, wherein the electric field is between 7.5 V/cm and 1000V/cm, wherein the onset of sintering is accompanied by a powerdissipation between 1 W and 100 W or from 10 to 1000 mWmm⁻³, wherein theonset of sintering is accompanied by a non-linear increase in theconductivity of the material, and wherein the time between the onset ofsintering and the completion of sintering is less than one minute.

In other embodiments, the material has a greater concentration ofnon-stoichiometric phase than Al₂O₃, wherein the Al₂O₃ is substantiallynot doped with MgO. The non-stoichiometric phases can beRuddlesden-Popper (RP) phases. In further embodiments, the material hasa greater concentration of non-stoichiometric phase than a materialselected from the group consisting of yttrium-stabilized zirconia,MgO-doped alumina, SrTiO₃ and Co₂MnO₄. The non-stoichiometric phases canbe Ruddlesden-Popper (RP) phases. In other embodiments, the material isselected from yttrium-stabilized zirconia, MgO-doped alumina, SrTiO₃ andCo₂MnO₄.

In certain embodiments, the material is provided in particles withaverage diameters between 60 nm and 1.5 μm, 60 nm and 200 nm or 1.0 μmand 1.5 μm.

In other embodiments, the method of sintering a material also includesexposing the material to a uniaxial force. The uniaxial force can bebetween 1.5 and 12 MPa.

The disclosure also provides a composition comprising material flashsintered according to the methods described herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts the enhancement of the rate of sintering in yttriastabilized zirconia (3YSZ) by DC electrical fields. An instabilityoccurs when the field is greater than a threshold value, estimated to beabout 40 Vcm⁻¹ in the present experiments, leading to sintering in justa few seconds at unusually low temperatures.

FIG. 2 depicts the phenomenon of flash sintering, which also manifestsin a power surge when the critical sintering temperature is reached,confirming that it is an instability in the process. The onset of thepower-instability coincides with the onset of Flash sintering shown inFIG. 1.

FIG. 3 shows that flash sintering is not seen when a field of 40 Vcm⁻¹is applied at the start of the sintering experiment, but it does occurif this field is applied when the furnace reaches 1150° C.

FIG. 4 depicts a field-assisted sintering apparatus.

FIG. 5 depicts dimensions of the “green sample” in mm. The thickness ofthe samples was 1.8 mm.

FIG. 6 depicts conventional sintering at a constant heating rate.

FIG. 7 depicts the influence of applied electric field on the sinteringbehavior of pure-alumina (a), and doped alumina (b), in experimentscarried out at a heating rate of 10° C. min-1.

FIG. 8 depicts Arrhenius plots for the power dissipation in thespecimens in MgO and pure-alumina at the high field, (a), and inMgO-alumina at different values of the applied field, (b).

FIG. 9 depicts the microstructures of flash sintered and conventionallysintered MgO-doped alumina.

FIG. 10 depicts linear-scale and log-scale plots of the current versusthe applied field for pure-alumina.

FIG. 11 depicts an Arrhenius plot of the conductivity of sintered pureAl2O3, measured under different dc fields.

FIG. 12 depicts current as a function of the dc field in sinteredMgO—Al2O3, at different temperatures.

FIG. 13 depicts an Arrhenius plot of the conductivity of sinteredMgO—Al2O3, measured under different dc fields.

FIG. 14 depicts current as a function of the time in sintered MgO dopedAl2O3, under a field of 25 to 250 V/cm, and 250 to 750 V/cm.

FIG. 15 depicts the cyclic, current-field response upon the applicationof field controlled cycles of increasing amplitude.

FIG. 16 is a line graph showing linear shrinkage with different appliedelectrical fields versus furnace temperature at constant heating rate of10° C./min.

FIG. 17 is an SEM image of the flash sintered SrTiO₃ at 500 V/cm. Flashsintering occurred at 900° C.

FIG. 18 is an SEM image of the flash sintered SrTiO₃ at 150 V/cm. Flashsintering occurred at around 1200° C.

FIG. 19 shows Arrhenius plots for the power dissipation in SrTiO₃samples at different values of the applied field.

FIG. 20 is an SEM image of the conventionally sintered SrTiO3 at 1400°C. for 1 h.

FIG. 21 is a line graph showing change in density (▪) and particle size(▴) of the SrTiO₃ sample with respect to furnace temperature. Voltage(dashed line) is given to show the experimental conditions.

FIG. 22A is a color-coded inverse pole figure map, generated withTSL/EDAX OIMTM. It shows the orientation and shape of the grainsobtained on flash sintered SrTiO₃ polycrystalline at 150 V/cm. Grainorientations with respect to the sample normal are colored according tothe standard stereographic triangle on the right.

FIG. 22B shows the area fraction of grains with respect to average graindiameter is plotted for representative areas of the flash sinteredSrTiO₃ at 150 V/cm.

FIG. 23A shows the color-coded inverse pole figure map, generated withTSL/EDAX OIMTM, shows the orientation and shape of the grains obtainedon conventionally sintered SrTiO₃ (0 V). Grain orientations with respectto the sample normal are colored according to the standard stereographictriangle on the right.

FIG. 23B shows the area fraction of grains with respect to average graindiameter is plotted for representative areas of the conventionallysintered SrTiO₃.

FIG. 24 is a line graph showing the photoinduced reflectivity dynamicsDR/R of conventionally and flash-sintered SrTiO₃ as a function of timedelay between pump and probe pulses. Single crystal SrTiO₃ is alsoanalyzed to compare polycrystalline samples with defect-free structure.

FIG. 25A is an XRD spectra of flash sintered and conventionally sinteredSrTiO₃. Starting powder is analyzed to reveal the structural differencesduring sintering process.

FIG. 25B shows peaks of all samples are given separately to demonstratethe peak shift toward high θ values.

FIG. 26 is a TEM image of flash sintered SrTiO₃ at 150 V/cm. Someregions contain Ruddlesden-Popper phases, caused by long-range orderlattice distortions.

FIG. 27 is an Arrhenius plot of the conductivity of flash sintered (□)and conventional sintered SrTiO3 (Δ). Reference (dash line-star) isgiven for comparison.

FIG. 28 is a schematic of the sinterforging experiment with externallyapplied dc electrical field.

FIG. 29 contains line graphs that show measurements of axial and radialstrains using a constant electric field of 100 V/cm, each linerepresents a different value of applied stress between 1.5 and 12 MPa.The x-axis is the furnace temperature in ° C.; this is the synonymouswith time since a constant heating rate of 10° C./min was employed.

FIG. 30 is a line graph showing the densification strains obtained fromthe axial and radial strain measurements in FIG. 29. The x-axis is thefurnace temperature in ° C.

FIG. 31 shows plots of the sintering rates in the flash-sinteringregime, derived from data given in FIG. 30. The rates decline tonegligible values once the specimens have reached full density. Thehorizontal axis is marked with both the furnace temperature and time.

FIG. 32 is a line graph that shows the shear strain obtained from theaxial and radial strain measurements in FIG. 2. The x-axis is thefurnace temperature in ° C.

FIG. 33 contains line graphs showing shear strain and volumetric strainusing a constant applied pressure of 5 MPa, and various electrical fieldstrengths 0-200 V/cm. The horizontal axis is the furnace temperature.

FIG. 34 is a plot of the volumetric power density versus inversetemperature. This figure shows the abrupt power surge accompanying theonset of flash sintering at various stresses.

FIG. 35 is a line graph showing the relationship between power surge anddensification in time-temperature domain during a constant heating rateexperiment. Input power is shown on the left y-axis and plotted with thedashed line. The densification strain is plotted on the right y-axis andshown with the solid line and triangles for each data point. Thehorizontal axis for all data is the furnace temperature.

FIG. 36 is a line graph showing measurement of the specimen temperaturewith a pyrometer during the power surge in a flash-sintering experiment,100 V/cm and 5 MPa. The input power is plotted on the left y-axis andshown with the dashed line. The Pyrometer measurement is plotted using asolid line and ‘x’, on the right y-axis. A straight line has been drawnto help show where the pyrometer temperature begins to deviate from thefurnace temperature.

FIG. 37 is a line graph showing an expanded view of the coupling betweenthe power surge and densification, with the pyrometer data from FIG. 36in the background (faint line with an “x”). The power data are shownwith the dashed line and the densification strain is shown as the solidline and triangle.

FIG. 38 is a plot of data according to Eq. (7), using the estimatedspecimen temperature noted in Table 2.

FIG. 39 is a scanning electron micrograph of a polished surface from aflash sinterforged specimen, showing uniform and equal-axis graindistribution.

FIG. 40 is the horizontal axis is the total field, plotted against thethreshold temperature for flash sintering.

FIG. 41 shows maps for estimating the specimen temperature given thefurnace temperature and the power dissipation in the specimen for fourdifferent values of the volume-to-surface ratio (V/A). The points A, Band C are from a simulation and experiments. A is from a simulation, Bfrom steady state power dissipation, and C from flash-sinterforgingexperiment. The model is based upon black body radiation.

FIG. 42 is a comparison of the black body radiation model withexperiments under steady state power dissipation in the specimen whilethe furnace temperature is held constant at 1250° C.

FIG. 43 contains line graphs showing the relationship between thepower-density and the specimen temperature in the time domain, in aflash-sinterforging experiment.

FIG. 44 is a line graph showing the relationship between power densityand sintering in the time domain in a flash-sintering experiment with3YSZ.

FIG. 45 is a line graph showing the relationship between specimentemperature and the sintering rate for three different values of theactivation energy for the coefficient for chemical diffusion. Forexample, a sample which sinters in an hour at 1400° C., would require atemperature of 1800° C. to sinter in 3.6 s, assuming an activationenergy of 500 kJ mol⁻¹.

FIG. 46 is an Arrhenius plot of the specific resistivity of the specimenas a function of the temperature.

FIG. 47 is a line graph showing shrinkage strain in the four particlesize specimens at 0 V and 100 V cm⁻¹, measured as the furnace is rampedup at a constant heating rate of 10° C. min⁻¹.

FIG. 48 is a line graph showing the sintering rates for the variousspecimens during flash sintering.

FIG. 49 contains line graphs showing field enhanced sintering at 20 Vcm⁻¹ in specimens of different particle size.

FIG. 50 shows Arrhenius plots for the power dissipation in the specimensin 3YSZ with different particle sizes at 20 V cm⁻¹ (field enhancedsintering) and 100 V cm⁻¹ (flash sintering).

FIG. 51 contains line graphs showing the power-density expended in thespecimen and the simultaneous measurement of the furnace temperaturewith a pyrometer. The specimen temperatures, as well as the powerdissipation in the current control regime are similar for all fourparticle-size specimens.

FIG. 52 shows the time-temperature relationship for the sintering ratebased upon the activation energy for chemical diffusion.

FIG. 53 shows micrographs of 1 μm conventionally and flash sinteredsamples. The dark shaded bar highlights the preponderance of nanosizegrains in the flash sintered case.

DETAILED DESCRIPTION

Dense ceramic bodies are traditionally produced by sintering greenpowder compacts at high temperatures. Sintering occurs by solid-statediffusion, which transports matter from grain boundaries into theneighboring pores. Thus the effective diffusion distance scales with thegrain size, while the rate of matter transport is determined byself-diffusion along the grain boundaries (at large grain sizes thetransport may become dominated by lattice diffusion, which is notrelevant to the present study). At the same time the driving force forsintering, which is proportional to the curvature of the pores, is alsoproportional to the grain size. As a result the rate of sintering isrelated to the grain size and to the diffusion coefficient, leading tothe following equation for the densification rate, {dot over (ρ)}¹:

$\begin{matrix}{\overset{.}{\rho} = {\frac{{Af}(\rho)}{{Td}^{4}}^{- \frac{Q_{B}}{RT}}}} & (1)\end{matrix}$

where A is a material constant, Q_(B) is the activation energy forself-diffusion at grain boundaries, ƒ(ρ) is a function of the density, Tis the temperature in K, and d is the grain size. The grain sizeexponent of 4 applies to boundary diffusion-dominated mass transport.Sintering is nearly always accompanied by significant grain growth,which slows the sintering process.

Techniques that use electromagnetic and electrical fields, in tandemwith time and temperature, have been shown to enhance the sinteringrate. These methods are collectively known as field-assisted sinteringtechniques (FAST)^(2,3,4). They include methods known as microwavesintering and Spark Plasma Sintering (SPS). However, a fundamentalunderstanding of the underlying atomistic mechanisms remains clouded.²Electrical sparks and plasmas at particle-particle contacts,self-cleaning of particles surfaces, and temperature-gradient-drivendiffusion have been proposed as explanations for field-enhancedsintering.⁵

Flash sintering is a novel technique for sintering materials in veryshort times and at lower temperatures compared to traditional sinteringmethods. The phenomenon of flash sintering is characterized by twoexperimental observations: (i) at a certain temperature and appliedelectrical field there is a sudden increase in the sintering rate suchthat sintering occurs in just a few seconds. A higher applied fieldlowers the temperature for the onset of flash sintering. (ii) Thesintering event is accompanied by a sharp increase in the conductivityof the ceramic, which occurs at the same temperature and applied field.

Thus, provided herein are methods of flash sintering. In one aspect,provided herein is a method of sintering a material, comprisingsimultaneously exposing the material to heat and to a DC, AC or pulsedelectrical field that is applied by a potential difference across thematerial, such that the material is sintered, wherein the time betweenthe onset of sintering and the completion of sintering is less than oneminute. In one embodiment of the method, the time between the onset ofsintering and the completion of sintering is less than 30 seconds. Inanother embodiment, the time between the onset of sintering and thecompletion of sintering is less than 5 seconds.

In certain embodiments of the methods described herein, the electricalfield is between 7.5 V/cm and 1000 V/cm. In other embodiments, theelectrical field is fixed and the heat is increased at a constant rate.In certain embodiments of the method, the heat is increased at a ratebetween 1° C. per minute to 100° C. per minute. In a particularembodiment, the heat is increased at a rate of 10° C. per minute.

In other embodiments of the methods described herein, the temperature ofthe furnace containing the material is fixed and the applied voltagefield is increased at a constant rate until the onset of sintering.

Flash sintering is different from nominal field-assisted sintering,where the application of fields leads to a gradual enhancement in thesintering rate. In the methods described herein, flash sintering occursabove a threshold field and temperature, (e.g. 850° C. and 120 Vcm⁻¹ foryttria-stabilized zirconia); while nominal field assisted sinteringoccurs at lower fields and higher temperatures^(15,16).

The hardware requirements for flash sintering are different from otherfield-assisted sintering methods including microwave sintering and SPS.In microwave sintering, the specimen is placed within a microwavechamber; often, collateral heating is used to sinter the specimen. InSPS the ceramic powder is placed within a graphite die and pressure isapplied, usually with a piston that is also constructed from graphite;then a high electrical current is applied to this assembly to heat thesample. Therefore the SPS method is driven by electrical currents ofseveral kiloamperes. In the flash sintering process neither microwavesnor a graphite die, nor electrical currents are used. Instead anelectrical voltage is applied by means of two electrodes across thespecimen. Therefore the flash sintering process is controlled by apotential difference rather than by electrical current. While theelectrical currents in the SPS process are much greater than onekiloampere, in flash sintering, the current is less than 10 amperes.Accordingly, in certain embodiments of the methods described herein, theelectrical voltage is applied to the material with two electrodes thatare electronically conducting. In a particular embodiment, theelectrodes are made from a metal or from an electronically conductingceramic material. In some embodiments, the electrodes are not physicallyin contact with the material.

Flash sintering has been demonstrated in several oxides including, cubicyttria doped zirconia (8YSZ)¹⁷, cobalt manganese oxide (Co₂MnO₄)¹⁸,titanium oxide (TiO₂) and strontium titanate (SrTiO₃)^(19,20).

Accordingly, in certain embodiments of the methods described herein, thematerial that is to be sintered is selected from yttrium-stabilizedzirconia, MgO-doped alumina, cubic yttria doped zirconia (8YSZ), cobaltmanganese oxide (Co₂MnO₄), titanium oxide (TiO₂) and strontium titanate(SrTiO₃). In other embodiments, the material is selected fromyttrium-stabilized zirconia, MgO-doped alumina, and Co₂MnO₄. In aparticular embodiment, the material is yttrium-stabilized zirconia(3YSZ). In another particular embodiment, the material is MgO-dopedalumina.

An immediate interpretation of flash sintering is that the Joule heatingof the specimen precipitated by the surge in power dissipation isresponsible for the very high rates of sintering. However, themeasurement of the temperature during the flash event (with an opticalpyrometer²¹) shows that the specimen remains far below the temperaturewhere the ceramic would have been expected to sinter in just a fewseconds. Thus, the power surge, and the surge in the sintering rate arenot linked by a cause-and-effect relationship; instead they appear toshare a common underlying mechanism. The exposition of this mechanism isthe main scientific challenge in the discovery of this new phenomenon.

Accordingly, in one embodiment of the methods described herein, theonset of sintering is accompanied by a sudden increase in the powerdissipated within the material, wherein the power dissipation ismanifested as a sudden increase in the current flowing through thematerial. In certain embodiments, the power dissipation is between 1 Wand 100 W. In other embodiments, the power dissipation is between 1 Wand 10 W, 10 W and 20 W, 20 W and 30 W, 30 W and 40 W, 40 W and 50 W, 50W and 60 W, 60 W and 70 W, 70 W and 80 W, 80 W and 90 W, 90 W and 100 W,1 W and 50 W, and 50 W and 100 W. In certain embodiments, the powerdissipation is about 1, 10, 20, 30, 40, 50, 60, 70, 80, 90 or 100 W. Ina particular embodiment (i.e., a bar-shaped specimen that is about 2 cmlong and 3 mm×2 mm in cross section) the onset of sintering isaccompanied by a power dissipation of about 1 W. As used in thiscontext, the term “about” may indicate ±0.5 W. Thus, in certainembodiments, the onset of sintering is accompanied by a powerdissipation of 1±0.5 W. More specifically, the term about may indicate±0.1 W. Thus, in other embodiments, the onset of sintering isaccompanied by a power dissipation of 1±0.1 W. In other embodiments ofthe methods, the onset of sintering is accompanied by a non-linearincrease in the conductivity of the material. In certain embodiments ofthe methods described herein, the onset of sintering is accompanied byan increase in the relative density of the material to 80-100% of thetheoretical density. In a particular embodiment, the onset of sinteringis accompanied by an increase in the relative density of the material togreater than 99% of the theoretical density.

Flash sintering is different from nominal field assisted sintering ofceramics. In field assisted sintering the rate of sintering is graduallyenhanced as the applied field is increased, whereas in flash sinteringthe event occurs precipitously. Nominal field assisted sintering inyttria doped zirconia has been successfully explained by the reducedrate of grain growth under the influence of an electrical field^(16,22).

The following possible mechanisms have been suggested for flashsintering:

1. Local heating at grain boundaries: local resistance atparticle-particle contacts can lead to higher local temperatures thatenhances diffusion¹⁵;2. Nucleation of Frenkel Pairs: nucleation of vacancy-interstitial pairsunder the applied field. The applied field can strip the charge on thevacancy and the interstitial (an electron on one and a hole on theother), leaving them charge neutral relative to the lattice. The biasfrom the sintering pressure can then draw the vacancy preferentiallyinto the grain boundaries and the interstitials into the pores,producing densification, while the electron-hole pair contributes tohigher electrical conductivity²³;3. Interaction between External Field and the Space Charge Field: thefield in the space charge layer adjacent to grain boundaries can havestrength of 10-1000 Vcm⁻¹. In other embodiments, the space charge layeradjacent to grain boundaries can have strength of 10-50 Vcm⁻¹, 50-100Vcm⁻¹, 100-150 Vcm⁻¹, 150-200 Vcm⁻¹, 200-250 Vcm⁻¹, 250-300 Vcm⁻¹,300-350 Vcm⁻¹, 350-400 Vcm⁻¹, 400-450 Vcm⁻¹, 450-500 Vcm⁻¹, 500-550Vcm⁻¹, 550-600 Vcm⁻¹, 600-650 Vcm⁻¹, 650-700 Vcm⁻¹, 700-750 Vcm⁻¹,750-800 Vcm⁻¹, 800-850 Vcm⁻¹, 850-900 Vcm⁻¹, 900-950 Vcm⁻¹, 950-1000Vcm⁻¹, 10-500 Vcm⁻¹ or 500-1000 Vcm⁻¹. These values are comparable tothe applied fields. The applied electric filed may interact nonlinearlywith the intrinsic fields, thereby changing the diffusion kinetics²³.

In a particular embodiment of the methods described herein, the methodcomprises simultaneously exposing the material to an electric field andto heat, such that the material is sintered, wherein the electricalfield is between 7.5 V/cm and 1000 V/cm, wherein the onset of sinteringis accompanied by a power dissipation between 1 W and 100 W, wherein theonset of sintering is accompanied by a non-linear increase in theconductivity of the material, and wherein the time between the onset ofsintering and the completion of sintering is less than one minute.

In certain embodiments, the sintering is completed in between 1 and 60seconds. In other embodiments, the sintering is completed in less than5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 or 60 seconds. In otherembodiments, the sintering is completed in between 1 and 10, 10 and 20,20 and 30, 30 and 40, 40 and 50, 50 and 60, 1 and 30 or 30 and 60seconds.

In other embodiments, the heat is increased at a constant rate untilonset of sintering. In certain embodiments, heat is increased at a ratebetween 1° C. per minute to 100° C. per minute. In other embodiments,heat is increased at a rate between 1° C. per minute to 10° C. perminute, 10° C. per minute to 20° C. per minute, 20° C. per minute to 30°C. per minute, 30° C. per minute to 40° C. per minute, 40° C. per minuteto 50° C. per minute, 50° C. per minute to 60° C. per minute, 60° C. perminute to 70° C. per minute, 70° C. per minute to 80° C. per minute, 80°C. per minute to 90° C. per minute, 90° C. per minute to 100° C. perminute, 1° C. per minute to 50° C. per minute, or 50° C. per minute to100° C. per minute.

In other embodiments, the sintering is accompanied by an increase in therelative density of the material to 80-100% of the theoretical density.In certain embodiments, the sintering is accompanied by an increase inthe relative density of the material to 80, 81, 82, 83, 84, 85, 86, 87,88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 or 100% of thetheoretical density. In other embodiments, the sintering is accompaniedby an increase in the relative density of the material to 80-85, 85-90,90-95 or 95-100% of the theoretical density.

In additional embodiments, the material has a relatively highconcentration of non-stoichiometric phase. This non-stoichiometric phasecan be a Ruddlesden-Popper (RP) phase. In certain embodiments, thematerial that is flash sintered has an amount of non-stoichiometricphase or Ruddlesden-Popper (RP) phase greater than the amount of thesephases present in Al₂O₃, wherein the Al₂O₃ is substantially not dopedwith MgO. In other embodiments, the material that is flash sintered hasan amount of non-stoichiometric phase or Ruddlesden-Popper (RP) phase110, 120, 130, 140, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600,650, 700, 750, 800, 850, 900, 1000, 2000, 3000, 4000 or 5000% greaterthan the amount of these phases present in Al₂O₃, wherein the Al₂O₃ issubstantially not doped with MgO.

In certain embodiments, the material that is flash sintered has anamount of non-stoichiometric phase or Ruddlesden-Popper (RP) phase aboutequal or greater than the amount of these phases present inyttrium-stabilized zirconia, MgO-doped alumina, SrTiO₃ or Co₂MnO₄. Inother embodiments, the material that is flash sintered has an amount ofnon-stoichiometric phase or Ruddlesden-Popper (RP) phase 75, 80, 85, 90,95, 100, 105, 110, 120, 130, 140, 150, 200, 250, 300, 350, 400, 450,500, 550, 600, 650, 700, 750, 800, 850, 900, 1000, 2000, 3000, 4000 or5000% greater than the amount of these phases present inyttrium-stabilized zirconia, MgO-doped alumina, SrTiO₃ or Co₂MnO₄.

In other embodiments, the size of the particles of material to be flashsintered are, on average, between 60 nm and 1.5 μm in diameter. Incertain embodiments, the size of the particles of material to be flashsintered are, on average, between 60 nm and 200 nm or 70 nm and 200 nmin diameter. In other embodiments, the size of the particles of materialto be flash sintered are, on average, less than 60, 100, 150, 200, 250,300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950,1000, 1050, 1100, 1150, 1200, 1250, 1300, 1350, 1400, 1450 or 1500 nm indiameter. In further embodiments, the size of the particles of materialto be flash sintered are, on average, between 60 and 100, 100 and 200,200 and 300, 300 and 400, 400 and 500, 500 and 600, 600 and 700, 700 and800, 800 and 900, 900 and 1000, 1000 and 1100, 1100 and 1200, 1200 and1300, 1300 and 1400, or 1400 and 1500 nm in diameter.

In other embodiments, the method of flash sintering also includeexposing the material to higher than atmospheric pressure. In certainembodiments, the higher than atmospheric pressure is between 1.5 and 12MPa. In other embodiments, the higher than atmospheric pressure isbetween 1.5 and 2.0, 2.0 and 2.5, 2.5 and 3.0, 3.0 and 3.5, 3.5 and 4.0,4.0 and 4.5, 4.5 and 5.0, 5.0 and 5.5, 5.5 and 6.0, 6.0 and 6.5, 6.5 and7.0, 7.0 and 7.5, 7.5 and 8.0, 8.0 and 8.5, 8.5 and 9.0, 9.0 and 9.5,9.5 and 10.0, 10.0 and 10.5, 10.5 and 11.0, 11.0 and 11.5, or 11.5 and12.0 MPa.

EXAMPLES Example 1 Flash Sintering of Nanograin Zirconia in <5 s at 850°C. Introduction

It has been shown that electrical fields of approximately 20 V/cm lowerthe sintering temperature of 3 mol % yttria-stabilized zirconia (3YSZ)from ˜1400° C. to 1300° C.^(6,7) This enhancement in the sintering ratecould be successfully explained by a slower rate of grain growth in thepresence of an electrical field.⁸ These papers document that electricalfields retard grain growth, which, as given by Eq. (1), can enhance therate of sintering.

The present work demonstrates that 3YSZ can be sintered in a few secondsat temperatures as low as 850° C. by increasing the field strength to˜100 V/cm. This unusual finding may be explained by local heating atgrain boundaries formed at the particle-particle junctions. It appearsthat this local heating can unleash a runaway process whereby heatingreduces the local resistance leading to more intense Joule heating, andso on. The end result is that the sample can be flash sintered in just afew seconds at a furnace temperature of just 850° C.

Methods

Commercial tetragonal 3YSZ powders (TZ-3YB, Tosoh USA, Grove City, Ohio)with a particle size of 60 nm were uniaxially pressed into dogbone-shaped specimens having a relative density of 50.4%. The gagesection had a length of 21 mm and a rectangular cross section of 3mm×1.58 mm. Sintering was performed in a vertical tubular furnace underthe application of a constant dc voltage. The sample was suspended inthe center of the tube by means of two platinum electrodes attached tothe handles of the dog bone specimens. A CCD camera recorded the sampledimensions through a series of optical filters positioned at the bottomend of the tube.⁹ Samples were sintered with the following heating ramp:21° C./min to 500° C., and then at a constant heating rate of 10° C./minup to 1450° C. or less, as needed to achieve full densification. Thetrue (linear) shrinkage strain, given by ∈=ln(l/l_(o)), where l_(o) isthe initial gage length and l is the time dependent gage length as thespecimen sinters. Because the experiments were carried out at a constantheating rate, time and temperature are proportional to one another.Thus, the results are presented by plotting the shrinkage strain as afunction of temperature.

Results

The sintering strain measured as a function of temperature, fordifferent values of the initial applied dc field, is reported in FIG. 1.These graphs show two regions: at low fields, <40 V/cm, densificationoccurs gradually, albeit at increasing rates as the field is increased.This regime is equivalent to the method called FAST sintering. At higherfields, sintering occurs almost instantly as recognized by the nearlyvertical slope of the shrinkage curves. In this regime, the onset ofsintering moves to a lower temperature as the field is increased from 60V/cm, eventually dropping to 850° C. when the field reaches to 120 V/cm.This nearly instantaneous sintering method is being called flashsintering. The rates of sintering given by the slopes of the strainversus time (or temperature, because the experiments were carried out aconstant heating rate of 10° C./min) are three orders of magnitudefaster in flash sintering regime than in FAST sintering. A plot of themeasured input power as a function of temperature yields an interestingfinding that is shown in FIG. 2. In the flash sintering regime (60-120V/cm), there is an abrupt increase in power dissipation at thetemperatures that correspond closely to the onset of flash sintering.Furthermore, the onset of the instability occurs at about the same powerlevel, about 1 W, irrespective of the applied field. At fields below 40V/cm, the power continues to increase monotonically as the temperatureincreases, as would be expected from the temperature dependence of ionicconductivity.

Discussion 1. Joule Heating at Grain Boundaries

We explore the hypothesis that local Joule heating at the grainboundaries, which form at the particle-particle contacts, is theunderlying cause for the onset of flash sintering. In a constant voltageexperiment, the power dissipation is given by V2/R, where V is theapplied voltage and R is the electrical resistance of the specimen. In afirst-order approximation, the total resistance can be written as a sumof the resistance of the crystal matrix, RC, and the grain boundaries,RGB. Therefore, the power (Watts) dissipated in the specimen is givenby:

$\begin{matrix}{W = \frac{V^{2}}{R_{C} + R_{GB}}} & (2)\end{matrix}$

If, in Eq. (2), RGB>>RC then power dissipation is dominated at the grainboundaries. A local rise in grain-boundary temperature would lower RGB,which, in turn, would impel greater power dissipation, thus leading tothe instability shown in FIG. 1. At the same time, an increasinggrain-boundary temperature would accelerate grain-boundary diffusionproducing ultrafast sintering. The explanation given above leaves twoquestions unanswered. First, the instability can be explained as well byJoule heating of the crystal matrix, because a rapid decrease in RCcould have the same consequence as a drop in RGB. The second question iswhy the effect is seen at higher fields but not at a lower appliedfield. One point of distinction between the low field and high fieldbehavior is that the onset of flash sintering begins below 1000° C.,while field-enhanced sintering (FAST) occurs above this temperature.This is also the temperature where the necks at particle-particlecontacts begin to grow.¹⁰ The runaway effect is more likely when Jouleheating can be concentrated at the boundaries, which is most likely whenthe contact area at particles is small and its resistance is high. Thiseffect was confirmed in an experiment where the sintering experiment wasstarted with zero field until reaching 1150° C., at which point a fieldof 40 V/cm was applied. As shown in FIG. 3, flash sintering occurredwhen the field was applied after reaching 1150° C., but not if appliedfrom the start of the experiment. The interpretation is that when thefield is applied from the start, some neck growth has occurred at 1150°C. (as shown by a shrinkage of ˜4%), which prevents the onset ofinstability. If the field is applied at 1150° C., then the absence ofneck growth means that interface resistance is high, which allows thefield to produce the instability.

2. Estimate of Grain Boundary Temperature

It is possible to estimate the local temperature at the grain boundariesby comparing the sintering rates (at the same density), by means of Eq.(1). The activation energy for self diffusion in 3YSZ is wellcharacterized from creep experiments, which like sintering, arecontrolled by grain boundary self diffusion¹². Its value ranges from480-533 kJmol⁻¹. We assume an average value of 500 kJmol⁻¹ for thefollowing analysis. Note that the sintering rate also depends on thedensity: this can be factored out by comparing the sintering ratesmeasured at the same density. The grain size in Eq. (1) is assumed toremain constant since grain growth is usually insignificant when theporosity remains interconnected (open porosity), as is the case whenrelative densities that are less than 0.8¹³.

We now apply Eq. (1) to estimate the grain boundary temperatures subjectto the constraints described above. If {dot over (ρ)}₀ is thedensification rate under zero applied field at temperature T₀, and {dotover (ρ)}_(E) is the densification rate measured under an applied field,both densification rates having been measured at the same relativedensity, then it follows from Eq. (1) that:

$\begin{matrix}{\mspace{20mu} {{{\ln \left( \frac{\text{?}T_{E}}{\text{?}T_{0}} \right)} = {\frac{Q_{B}}{R}\left( {\frac{1}{T_{E}} - \frac{1}{T_{0}}} \right)}}{\text{?}\text{indicates text missing or illegible when filed}}}} & (3)\end{matrix}$

where the activation energy for self diffusion, Q_(B)=500 kJmol⁻¹. Theeffective grain boundary temperature, T_(E), can now be estimated fromEq. (3). The values for T_(E) for different densities calculated in thisway are given in Table 1. The top row gives the values for the furnacetemperatures corresponding to five levels of relative density, rangingfrom 0.55 to 0.75, without an applied field. The values with the appliedfield refer, on the left, to the furnace temperature, T₀, and on theright to the estimated grain boundary temperature, T_(E). The data areseparated into two segments, the upper set referring to FAST sinteringand the lower set to Flash sintering.

Consider first the FAST sintering data. Here the estimated grainboundary temperatures, with an applied field, are close to the furnacetemperature without the applied field. For example for ρ=0.65 thefurnace temperature without the applied field is 1334° C., whereas inFAST sintering the estimated temperature is 1345° C. at 20 Vcm⁻¹ and1365° C. at 40 Vcm⁻¹. The reasonable agreement between the estimatedtemperature (with the field) and the measured temperature (without thefield) is satisfying.

In the case of flash sintering the estimated grain boundary temperaturesincrease dramatically. The difference between the estimated and thefurnace temperature increases to 350° C. at a field of 60 Vcm⁻¹, and to850° C. at a field of 100 Vcm⁻¹.

Estimate of Joule Heating by Power Dissipation and Black Body Radiation

If specimen is considered as a monolithic body, which heats upuniformly, then the rise in temperature may be calculated by equatingblack body radiation to the power dissipation in the specimen by theapplied field. The analysis leads to the following equation⁶:

$\begin{matrix}{\frac{\Delta \; T}{T_{o}} = \frac{W}{4A\; \sigma \; T_{o}^{4}}} & (4)\end{matrix}$

Here ΔT is the increase in the temperature of the body due to Jouledissipation of electrical energy, given by W. The total surface area ofthe specimen (assumed to be the gage section) is equal to A, and σ isthe black body radiation constant equal to σ=5.67*10⁻⁸Wm²K⁻⁴. As before,the furnace temperature is given by T₀. For our experiments A=1.9*10⁻⁴m². Substituting the range of values from the experiments, the increasein the specimen temperature is predicted to no greater than 10° C., muchless than the estimated increase in the grain boundary temperature.

The discussion above draws a distinction between field assistedsintering of ceramics and metals. Refractory metals, e.g. Mo and W, aresintered, even today, by electrical resistive heating, as taught in apatent dating back to 1906¹⁴. In these experiments the primary functionof the applied fields is to heat the entire specimen directly withelectrical currents: a mechanism quite different from the proposed localheating of grain boundaries in ceramics

3. Closing Remarks

The results in FIG. 1 draw a distinction between FAST sintering, wherethere is a gradual increase in the sintering rate with applied field,and flash sintering where sintering occurs nearly instantaneously abovea threshold value of the applied field, at remarkably low temperatures.The field enhanced sintering in the FAST regime has been successfullyexplained in terms of the effect of and electrical field on reduced rateof grain growth⁶. However, the grain size of the sample that was flashsintered at 850° C. was measured to be 150 nm (first by SEM and thenconfirmed by TEM), not remarkably different from the grain size inspecimens sintered by the FAST method. The inference is that flashsintering is not due to reduced grain size under the applied field, butdue to enhanced kinetics, which has led us to propose a rapid rise atgrain boundaries as a possible mechanism for flash sintering. It wouldbe a mistake to discard other possible mechanisms for this unusualbehavior, for example the kinetics may be enhanced by the “nucleation”of Frenkel defects (vacancy interstitial pairs) under the driving forceof an applied electrical field. Alternatively, the high applied fieldsmay interact nonlinearly with the intrinsic fields present across thespace charge layers adjacent to grain boundaries, thereby producing acatastrophic change in self diffusion at grain boundaries.

It is well to keep in mind that platinum electrodes are blocking, thatis they transport electrons, not oxygen ions. At the cathode the neutraloxygen must be reduced to oxygen ions. If the currents are so large thatthe oxygen cannot be replenished from the environment, or if theenvironment is essentially inert, then high fields and currents canproduce electrolytic reduction of the oxide, which can be seen asblackening of zirconia near the cathode. In the present experiments suchblackening was not observed.

Conclusions

The flash sintering phenomenon is expressed by a sudden sintering eventwhen a certain temperature is reached for a given applied field. In 3YSZwe find that the fields must be greater than a critical value, above 40Vcm⁻¹. As the field is increased the temperature for the onset of flashsintering becomes lower and lower. In the present experiments, 3YSZspecimens could be sintered in a few seconds at 850° C. at a field of120 Vcm⁻¹. The proposed mechanism for flash sintering is preferentialJoule heating at the grain boundaries, especially when initiated in theearly stages of sintering when particle-particle contacts are justbeginning to develop. When the relationship between the sintering rateand temperature is applied to the data, then grain boundary temperaturethat is 585° C. above the furnace temperature is estimated for anapplied field of 100 Vcm⁻¹. The energy input to induce flash sinteringis only 1 W, which translates into a temperature rise of 10° C. in thespecimen as a whole when analyzed by black body radiation, far below theestimated increase in the grain boundary temperature. Flash sintering,can lead to considerable energy savings in the processing of ceramics.

TABLE 1 Table 1: Estimates of grain boundary temperature, T_(E), atdifferent applied electric fields at different values of relativedensity, ρ. The temperature T₀ refers to the grain boundary temperaturewithout an applied field. The top row refers to the zero field case, andthe data refer to the furnace temperatures at different values of thedensity. All experiments were carried out at a constant heating rate of10° C. min⁻¹. Field ρ = 0.55 ρ = 0.60 ρ = 0.65 ρ = 0.70 ρ = 0.75 T₀T_(E) T₀ T_(E) T₀ T_(E) T₀ T_(E) T₀ T_(E) V cm⁻¹ ° C. ° C. ° C. ° C. °C. ° C. ° C. ° C. ° C. ° C. 0 1244 1303 1334 1362 1387 “FAST” Sintering20 1195 1247 1237 1315 1265 1345 1288 1388 1301 1421 40 1138 1252 11751324 1195 1365 1208 1398 1219 1434 Flash Sintering 60 1014 1358 10171454 1018 1494 1020 1541 1020 1577 75 990 1417 991 1532 991 1571 9911607 991 1641 90 935 1428 935 1561 936 1608 936 1649 936 1689 100 9121470 912 1636 912 1683 912 1730 912 1770

Example 2 Field Assisted and Flash Sintering of Alumina and itsRelationship to Conductivity and Mg—O Doping Introduction

In the present work we study the applicability of flash sintering toalumina, which, in contrast to the materials studied so far¹⁵⁻²¹ is apoor electrical conductor. We show that fields higher than 500 V/cmtrigger flash sintering in MgO-doped alumina, while the same fields havelittle effect on the sintering of pure-alumina. As was the case in otherceramics¹⁵⁻²¹, the onset of flash sintering in alumina is accompanied bya surge in the current. Therefore, phenomenologically speaking,MgO-doped alumina and yttria doped zirconia show the same “flash” effecteven though one is essentially a stoichiometric compound while the otheris highly non-stoichiometric.

Experimental 1. Flash Sintering

The setup for the flash sintering experiments¹⁵ is sketched in FIG. 4.This method is adapted from conventional sintering: the difference beingthat an electric field is applied by means of two platinum electrodes.The electrodes wires also serve the purpose of suspending the specimeninto the hot-zone of the furnace. The change in the physical size of thesample is measured from pictures acquired with a CCD camera through anoptical low pass filter and a silica window²⁴. The shrinkage strain wascalculated as the true strain, ∈=ln(l/l_(o)), where l is the timedependent gage-length and l_(o) is the initial gage length.

In the present experiments a constant voltage was applied to thespecimen, while the furnace temperature was increased at 10° C./min upto 1400° C., followed by an isothermal hold of 1 h. The current waslimited at the power supply to 60 mA. Often flash sintering is seenduring the ramp-up in the furnace temperature; the voltage supply wasturned off just after this event.

2. Materials

The starting powder was AKP-50, High Purity Alumina from Sumitomo,specified to be >99.99% pure, and having a particle size of 100-300 nmThe powders were used either as-received, or doped with 0.25 wt % MgO.The doping was performed by adding the powder to a solution of magnesiumnitrate and distilled deionized water. The suspension was dried andground in a mortar. The powder (doped or as received) was mixed with 5wt % polyvinyl alcohol (mw 49000, Fluka) in water. The slurry was driedat 90° C. in an oven and ground to a powder in mortar and pestle. Theresulting powder was uniaxially pressed at 280 MPa in a dog bone shapeddie, to a green density of 0.55±0.01 of the theoretical density ofα-Al₂O₃ (3.99 gcm⁻³). The dimensions of the cold-pressed, green sampleare given in FIG. 5.

For clarity, form here onwards the MgO-doped alumina is referred to assimply MgO-alumina. Experiments were also carried out with undoped,nominally pure-alumina. In these cases the material is simply calledpure-alumina.

3. DC Electrical Conductivity

The electrical current, or the dc electrical conductivity was measuredin different types of experiments: (i) in the powder performs during thesintering process, (ii) in samples that had been sintered to fulldensity by conventional sintering prior to the measurement of theconductivity, and (iii) by applying electrical fields of differentamplitudes to samples prepared by conventional sintering, both as theapplied fields were ramped up into the non-linear regime, and thenlowered back down. The purpose of the last set of experiments was todetermine if the non-linear increase in conductivity created defectsthat left a residual effect in the ceramic.

The temperature of the samples was raised (and then lowered) in steps of50° C. between the range of 800° C. and 1400° C., taking care thatsteady state current was achieved at each temperature before themeasurement was taken, which usually occurred within 10 s. In someinstances the field was applied for longer times, to study the currentversus time profile. The specific conductivity is calculated accordingto the following relation:

$\begin{matrix}{\sigma = \frac{il}{Vwt}} & (5)\end{matrix}$

Where i is the measured current, V is the applied voltage, l the length,and w and t the width and the thickness of the gage section. Theconductivity is calculated according to Eq. 5, by simplifying thegeometry of the gage section to a constant cross section with initialdimensions of 3.3×1.8×20 mm.

The conductivity was measured in the two electrode configuration insteadof the four point method, because it was difficult to apply fourelectrodes to a green sample undergoing sintering. The two electrodestest method is less accurate than the four point method because itincludes the contact resistance. However, the two electrode method islikely to be valid provided the current reaches a steady state atconstant field. Results reported later in the paper show that the steadystate was reached in just a few seconds in the Ohmic regime. Also, thevalues of the conductivity we measure fall well within the nominal rangereported in the literature^(25,26).

4. Microstructure

The grain size was measured from images taken with a JSM-7401F fieldemission SEM (JEOL). Specimens were prepared by thermal etching for 30min at 1100° C., followed by coating with a with a 2 nm layer of Au—Pd.The mean grain size was determined by the linear intercept method, witha correction factor of 1.56.

Measurements of Strain and Conductivity During the Sintering Process

1. Conventional Sintering (without Field)

The shrinkage strain versus temperature data for nominally pure andMgO-alumina without applied field (at 0V) are given in FIG. 6. Thetemperature was ramped up to 1400° C. at a heating rate of 10° C.min⁻¹and then held at that temperature for 60 min. In both cases the finaldensity is reached at a shrinkage strain of −0.18 which occurs at aboutmid-way during the holding period at 1400° C. Both pure and MgO-aluminashow similar sintering behavior. In the intermediate regime the dopinghas the effect of slightly delaying the sintering rate (upon reaching1400° C., the shrinkage of pure and MgO—Al₂O₃ are −0.135 and −0.115,respectively). However after 1 h isothermal hold, the sintering curvesmerge and the final shrinkage strains are nearly the same (−0.180 versus−0.178).

The use of MgO as a dopant is known to eliminate intragranular pores andrefine the grain size, producing translucent alumina²⁷. The effect ofMgO on sintering rate is not new: in conventional sintering²⁸, two stepssintering²⁹ and in spark plasma sintering³⁰, MgO was observed toslightly retard densification in the intermediate stage of sintering,but to have a positive effect in the last stage of sintering. Thesegregation of MgO to grain boundaries is believe to retard the initialshrinkage²⁸, and accelerate the final shrinkage²⁸ by preventing thebreakaway of pores from the grain boundaries during grain growth³¹.

2. Field Assisted Sintering

The shrinkage curves for constant heating rate (10° C.min⁻¹) experimentsare reported in FIG. 7. These experiments did not include an isothermalhold at 1400° C. The data for pure-alumina is given on the left infigure (a), which are compared to the data for MgO-alumina on the rightin (b). The data for 0V (without field) is compared to the shrinkagebehavior at field strengths of 250-1000 Vcm⁻¹.

The data for pure-alumina in FIG. 7( a) shows that the sinteringbehavior with a field of 1000 Vcm⁻¹ is only very slightly higher thanthe sintering rate obtained in conventional sintering (without appliedfield). In either case full density is not reached at the end of theramp up to 1400° C. (the microstructure confirms a porous structure).The shrinkage strains at the end of the experiments were −0.135 with thefield, and 0.148 without the electrical field.

In contrast to pure-alumina, the dc field has a remarkable effect on thesintering of MgO—Al₂O₃. Three sets of data are given, at 250 Vcm⁻¹, 500Vcm⁻¹ and 1000 Vcm⁻¹. The effect of the field is minor at 250 Vcm⁻¹,with a strain of only −0.124 being achieved at 1400° C. But at higherfields flash sintering^(15,17,18,21) is observed. At 500 Vcm⁻¹ fulldensification strain of −0.182 is obtained at 1320° C., and at 1000Vcm⁻¹ densification occurs at just 1260° C. The shape of the sinteringcurves are noteworthy in that sintering follows the behavior seen inconventional sintering in FIG. 7( a), until the “flash event”, when thesintering curves assume a nearly vertical posture, with fulldensification achieved within a few seconds. However, the curve for 500Vcm⁻¹ suggests an incubation time for the onset of flash sintering,which is nearly absent, or very brief, at 1000 Vcm⁻¹. It is possiblethat a slower rate of heating would shorten the incubation time. At 10°C.min⁻¹ the lowest field for inducing flash sintering appears to be ˜500Vcm⁻¹, but it may be that lower heating rates can induce flash sinteringat lower fields.

3. Power Dissipation

The power dissipation in the specimen is equal to the product of theapplied voltage and the current flowing through the specimen. In earlierexperiments with other oxides^(15,18) we have found that the onset offlash sintering is accompanied by a surge in power dissipation. Thepresent experiments are consistent with this behavior. The data areplotted in Arrhenius form since the increase in (steady state) currentwith temperature is expected to be thermally activated, which, given aconstant value for the activation energy, would appear as a straightline with a negative slope, since the experiments are carried out at aconstant applied voltage. (This assumption is not strictly correct sincethe length and the cross-section of the specimen, as well as itsporosity are changing as the sample sinters. However, the errors tend tocancel: for example while the gage length becomes shorter which wouldincrease the specific conductivity, the cross section also shrinks whichwould decrease the conductivity. Although the cross-section decreasesthe conductivity at twice the rate as the length increases it—becausethe cross-sectional strain is twice the linear strain—this difference isfurther compensated by the reduction in porosity which would tend toincrease the conductivity. These compensating effects justify the use ofthe initial dimensions of the specimen as an approximate estimate of thespecific conductivity of the specimen while it sinters.)

We recall from FIG. 7 that a field of 1000 Vcm⁻¹ had little effect onthe sintering behavior of pure-alumina, while it induced flash sinteringat ˜1260° C. in MgO doped-alumina. This behavior is reflected in theArrhenius plots of power-dissipation shown in FIG. 8 b. While thepure-alumina follows an essentially Arrhenius behavior, the MgO-aluminaexhibits a power surge that coincides with the onset of flash sintering.The power dissipation curves for lower fields in MgO-alumina are givenin FIG. 8 b. A sharp increase in power-dissipation is seen at 500 Vcm⁻¹,where flash sintering is seen, but not at 250 Vcm⁻¹, which did notappear to induce flash behavior. However, the slope of the curve at 250Vcm⁻¹ deviates from linearity, unlike the data for the pure-alumina at1000 Vcm⁻¹ given FIG. 8( a). This result suggests the onset ofnon-linear behavior to some degree at 250 Vcm⁻¹, but not strong enoughto precipitate flash sintering which occurs when the field is increasedto >500 Vcm⁻¹. The hesitation in the power surge is evident even at 500Vcm⁻¹; it may reflect an incubation time for the onset of flashsintering seen in FIG. 7( b). In this respect that data appear to have adifferent exposition as compared to the earlier experiments with yttriadoped zirconia where flash sintering occurred abruptly without aninkling of an incubation time.

Finally it is to be noted that application of 1000 Vcm⁻¹ to thepure-alumina sample led to arcing and unstable conductivity when 1400°C. was reached. Perhaps the arcing would also have occurred in theMgO-alumina sample had it been ramped up to 1400° C., but did notbecause sintering was completed at a lower temperature.

4. Microstructure

The microstructure of the specimens was examined in a scanning electronmicroscope.

Specimens were prepared by thermal etching (30 min at 1100° C.) of thepolished cross-section, followed by thin coating of Au—Pd. Two results(for MgO-doped alumina) are reported here. Both specimens had beensintered to full density, one in the conventional way, without anapplied field at 1550° C. for 1 h, and the other flash sintered at 1000Vcm⁻¹ at 1260° C. The micrograph from the flash sintered specimen isshown in FIG. 9( a), and from the conventionally sintered specimen inFIG. 9( b). The conventionally sintered specimen had an average grainsize of 1.9 μm, while the flash sintered specimen had a smaller grainsize of 0.8 μm.

Conductivity of Fully Dense, Conventionally Sintered Specimens

The measurements reported in this section were carried out on samplesthat had been sintered to full density, with and without MgO doping, at1550° C. for 1 h, by conventional sintering. The green samples had thesame shape as shown in FIG. 5, they were sintered without electric fieldin the same furnace configuration as in FIG. 4. The electricalconductivity was measured through the platinum wire electrodes attachedto the specimen in the usual way.

The experiments were carried out by a stepwise increase in thetemperature. At a given temperature the current was measured atdifferent levels of the applied voltage. At each voltage the current wasmeasured after it had reached a steady state, which usually happened inless than 25 s (but not in doped specimens at high fields, as explainedlater). In this way not only the effect of the temperature, but alsonon-linear (deviation from Ohmic) behavior, at higher fields, could bemeasured. Since the physical dimensions of the specimens were the samefor all experiments, the measurement of the current and voltage areequivalent to the specific conductivity as prescribed by Eq. (5). Thecurrent at a given voltage was measured by holding the field constantfor 25 s. The field was then removed for 5 s before stepping up (ordown) to the measurement at the next voltage.

The most notable aspect of the results presented here is thenon-linearity of the conductivity when they data are plotted with theexpectation of Arrhenius behavior. Normally such a plot would exhibitlinear behavior reflecting the following equation:

$\begin{matrix}{\sigma = {A\; ^{({- \frac{Q}{RT}})}}} & (6)\end{matrix}$

where σ is the conductivity, and Q is the activation energy for theconduction mechanism. Therefore, nominally, an Arrhenius plot of theconductivity yields a straight line with a slope that is a measure ofthe activation energy.

As reported below we see a stark difference between the Arrhenius plotsfor MgO-doped and pure-alumina. These plots are similar to thepower-surges that were measured while the specimens were being sinteredunder an electrical field (FIG. 8). That this non-linearity is also seenin specimens that had been fully sintered in the conventional way provesthat the non-linear power surge is not the cause of flash sintering, butrather, it represents a phenomenon that shares the same mechanism asflash sintering.

The non-linear behavior seen in the doped specimens (as described justabove) was followed by measurements of the conductivity by firstincreasing and then decreasing the electrical field. The amplitude ofthe field was varied to assess the reversibility of the conductivity,especially when the amplitude was large enough to enter the non-linearregime. We see a remarkably high residual conductivity in specimens thathad been subjected to high fields, suggesting that the non-linearity isaccompanied by the nucleation of new charged defects, which survive whenthe current is measured again at lower applied fields.

The results below are reported in the following sequence: they startwith the conductivity of pure-alumina, followed by the behavior ofMgO-alumina, and finally results showing the residual conductivity inMgO-alumina which had been exposed to cyclic electrical fields arepresented.

1. Conductivity of Pure-Alumina

The current-field (the I-V) plots for pure specimens at temperaturesfrom 900° C. to 1400° C., in steps of 100° C., are given in FIG. 10.Plots using linear axes are shown on the left, and those withlogarithmic axes on the right. The electric fields range up to 1000Vcm⁻¹, the same range that was used in the sintering experiments. At alltemperatures, and for the full range of the electrical fields the plotsare essentially linear. The non-linearity may be defined by theparameter α in the following equation:

i∝E ^(α)  (7)

where α≈1 implies linear behavior. The plots in FIG. 10( a) show smallnon-linearity at fields greater than 500 Vcm⁻¹, which is likely fromsome Joule heating in the specimen. The log-log plots in FIG. 10( b),however, cannot distinguish the small non-linearity that is evident in(a).

The upward shift in the lines in the log-log plot as the temperature isincreased reflects thermally activated conduction of charged defects.The Arrhenius plot of the conductivity at different temperatures isgiven in FIG. 11. All data fit into a reasonable straight line, whoseslope yields and activation energy in the 150-207 kJmol⁻¹ range. Notethis low value of the activation energy most likely precludes thepossibility of ionic diffusion. In high likelihood, the conductivitiesbeing measured here are electronic conductivities. Since the metalelectrodes do not block the transport of electrons across themetal-ceramic interface, we expect to reach the steady state currentrather quickly, which was indeed the case (in less than a few seconds).

2. Conductivity of MgO-Doped Alumina in Dense Samples

The measurements of the conductivity in MgO-alumina was complicated bythe non-linear behavior at fields greater than ˜250 Vcm⁻¹. In thenon-linear regime a steady state value for the current could not beachieved within 25 s, indeed the current continued to increase withtime. The field was increased in steps up to 750 Vcm⁻¹. A dead period of5 s was allowed between one field and the step up to the next field. Attemperatures above 1200° C. and high fields, the current does not reacha steady state but increased steadily to the maximum allowed by thepower supply (60 mA). These “cut-off”, non-steady state currents arereported as solid data points in FIG. 13.

The linear-scale and log-log plots for the current versus field aregiven in FIG. 13. They show that the behavior is essentially linearbelow ˜200 Vcm⁻¹, and non-linear above this field, regardless of thetemperature. The temperature was varied from 800° C. to 1400° C.

Because of the wide spread in the values of the current, arising fromthe non-linear behavior, the log-log plots are more definitive inshowing the transition to from linear to non-linear behavior. Note thatthe value for α≈1 in the linear regime, but increases to α≧3 in thenon-linear regime. The slopes are temperature independent, and thetransition between quasi-ohmic and non-ohmic conductions appears alwaysat the same field intensity, regardless of the temperature. Theseresults, for MgO-alumina, stand in contrast to the measurements forpure-alumina, that were reported in FIG. 11, where the behavior remainedlinear throughout the range of the applied field, at all temperatures.

The Arrhenius plot for the conductivity for MgO-alumina is shown in FIG.13. It is to be contrasted to the data for pure-alumina that waspresented in FIG. 11. The contrast is remarkable. Whereas, all thepoints, obtained at various levels of applied field, converge to asingle line in pure-alumina, in the case of MgO-alumina the pointsspread out to different lines for different applied fields. However, theslopes for all the linear plots for MgO-alumina are the same as forpure-alumina, yielding similar activation energies. For MgO-alumina theactivation energies lie in the range of 155-222 kJmol⁻¹, while forpure-alumina they fall between 150-207 kJmol⁻¹. There is a hint of twoslopes at fields below 500 Vcm⁻¹ —155 kJmol⁻¹ below 1050° C. and 220kJmol⁻¹ above 1050° C.—but the difference is not large enough to bedefinitive. At higher fields (above 500 Vcm⁻¹) the data fit nicely to asingle straight line throughout the temperature range with an activationenergy of 210 kJmol⁻¹.

The most significant distinction between the Arrhenius plots for pureand MgO-alumina is the dispersion in the lines for the data at differentfields for MgO-alumina, but the coalescence of the data into a singleline for the pure-alumina. In the doped case the lines move to highervalues of the current as the field is increased. Despite the dispersionin the lines, the activation energies remain the same for allmeasurements. The results, therefore, show that the pre-exponential inEq. (6) changes with the field in the MgO-alumina, but remains constantfor pure-alumina. Since Q reflects the activation barrier for themobility of the charged defects, while the pre-exponential is related tothe concentration of the defects, we infer that the field has the effectof increasing the concentration of defects in MgO-alumina. This effectappears to be more pronounced above 500 Vcm⁻¹, where there is a greaterdispersion of the lines for the data in FIG. 12 b, than below thisfield.

3. Residual Conductivity after Cycling MgO-Alumina into the Non-LinearRegime

We have hypothesized that the onset of non-linearity in conductivityarises from the increase in the defect concentration which enhances thepre-exponential in Eq. (6). If this is the case then it is also likelythat some fraction of these defect concentrations survive when theapplied field is traversed downwards. The results from these experimentsare reported in this section. Indeed, they show considerable residualconductivity when the samples are cycled between increasing anddecreasing applied fields. This effect is seen only in the MgO-alumina;this is self-evident since pure-alumina did not exhibit non-linearincreases in conductivity at high fields.

The time dependent change in the current, in a specimen held at 1300°C., when the applied field is first increased in steps, up to 750 Vcm⁻¹,and then stepped downwards, are given in FIG. 14. The field is held for25 s at a given field, which is followed by a dead period of 5 s beforethe next step in the field is applied. The data are divided into twofigures, the one on the left covers currents from 0-1 mA and the one onthe right from 0-60 mA. The results for fields up to 250 Vcm⁻¹ are shownin the first figure and those for fields up to 750 Vcm⁻¹ in the secondfigure.

In the low field regime (up to 250 V⁻¹) the current usually decreasesafter the application of the field before settling down to a steadystate. However, at fields ≧500 Vcm⁻¹, the current continues to increasewith time.

The data given on the right in FIG. 14, show the current-time profilewhen the applied field is stepped down from 750 Vcm⁻¹ to 500 Vcm⁻¹, andthen to 375 Vcm⁻¹, and finally down to 250 Vcm⁻¹. Note the much highercurrents at these lower fields than were seen when the fields were beingstepped upwards.

The hysteretic behavior described above is absent if the sample is notexposed to the non-linear regime. The results in FIG. 13 show thecurrent-field behavior when the sample is cycled up and down in theapplied field (here the applied voltage was changed continuously at arate of 30 Vs⁻¹). These experiments were carried out at 1300° C., and arest period of 30 s was allowed between the cycles. Three types ofcycles were employed. In the first type the sample was raised to a fieldof 750 Vcm⁻¹, in the second type of cycles the amplitude of the fieldwas 600 Vcm⁻¹, and in the third kind the maximum value of the field waslimited to 300 Vcm⁻¹. For the 750 Vcm⁻¹ case the current was cut-off at60 mA (by the power supply) which is the reason for the “flat-top” forthe value of the current. Note that the current is much higher duringramp-down than during the ramp-up part of the cycle. A similar behavior,though less severe, is seen when the field-amplitude was 600 Vcm⁻¹.However, the behavior is linear and reversible when the amplitude washeld at 300 Vcm⁻¹. An expanded view of the data in the lower left cornerof FIG. 15 a is given on the right in FIG. 15 b: it more clearly showsthe linear and reversible behavior at low field-amplitude. Thehysteretic behavior at the higher fields may not be attributed to Jouleheating since the transition from reversible to hysteretic shape of thecycles changes abruptly at a field of ˜200 Vcm⁻¹. The supposition isthat defects introduced at the high fields lead to higher residualconductivity when the fields are brought back down.

Discussion of Conductivity of Alumina from the Literature

The measurement of dc electrical conductivity of pure and MgO-dopedalumina at high temperatures and high fields are unusual. They pointtowards electrons being the dominant transport species in both cases. Abrief review of the reports from the literature is appropriate to givecontext to these measurements.

The values for dc conductivity of alumina reported in the literaturevary over a wide range, and appear to depend greatly on purity andprocessing conditions²⁶. Furthermore, the mechanism of conduction andthe dominant charge carrier in Al₂O₃ have often been debated. In singlecrystal alumina it has been claimed to be predominantly electronic,ionic or mixed, and to depend on the temperature and oxygen partialpressure. For example, MgO doped Al₂O₃ single crystals have beenreported to be electronic conductors at low temperatures and mixed ionicand electronic conductors at the higher temperatures and low p_(O2) ³².At high temperatures the ionic conduction is explained by Alinterstitials³³ or oxygen vacancies at low p_(O2), while the electronicconduction is dominated by holes³⁴. More recent results attribute only0.3% of the conductivity in pure single crystals at 1200° C. to arisefrom ionic diffusion³⁵. The measurement of the activation energy in thepresent experiments suggest electronic conductivity in both doped andpure-alumina at fields up to 200 Vcm⁻¹ in the temperature range of800-1400° C.

The non-linear conductivity of MgO-doped alumina seen at fields 250-1000Vcm⁻¹ at temperatures up to 1400° C., as measured in the presentexperiments, has not (to our knowledge) been reported in the literature,although a non-linear I-V behavior has been seen in thin films ofalumina at low temperatures. In a recent paper, Talibi³⁶ shows atransition from Ohmic to “superOhmic” behavior in 0.65 nm thick 96% pureAl₂O₃ film at low temperatures, but at fields much higher than thoseemployed in the current experiments. The transition point was nottemperature independent as in the present case, but varied from 170kVcm⁻¹ at room temperature to 50 kVcm⁻¹ at 170° C. The non-linearity wasexplained by space charge limited conduction. In a different study on490 nm thick films of porous alumina the transition from quasi-Ohmic tosuperOhmic behavior was observed at 204 kVcm⁻¹ at room temperature³⁷.The conduction mechanism was attributed to electron-hopping at lowfields, and space charge limited conduction in the high field regime.

The conductivity in alumina is also known to increase in the presence ofionizing radiation^(38,39). The radiation induced conductivity (RIC), orradiation induced degradation (RID), increased dramatically at fieldsabove a threshold of 500 Vcm⁻¹ ³⁹. This result was explained by anincrease in the stable F-center production rate by means of either anincrease in the primary vacancy-interstitial production rate or adecrease in the recombination rate³⁹. This non-linear effect of thefields on conductivity at fields similar to those in the currentexperiments is to be noted, as is the equivalence between the nature ofradiation damage and the nucleation of Frenkel pairs that is postulatedto explain flash sintering.

An interesting effect of a dc field on the conductivity of MgO has beenwell documented⁴⁰⁻⁴². A field of 1000 Vcm⁻¹ was applied for ˜100 h at1200° C. The conductivity of MgO remained constant at first, but thenstarted to increase eventually by three orders of magnitude leading toJoule heating and electrical breakdown. This incubation time for theincrease in conductivity was explained by the piling up of cationimpurities and lattice defects in the vicinity of dislocations and smallangle grain boundaries. Perhaps a similar aggregation of defects alongthe grain boundaries in Al₂O₃ could have been responsible for theresults reported from the current experiments.

Summary

Pure-alumina, of nominal purity does not show field-assisted sinteringunder the conditions where MgO-doped alumina does. It may be possiblethat higher fields and temperatures could have produced flash sinteringin pure-alumina. However, the maximum field and temperature that may beused would be limited by dielectric breakdown and arcing, which wasobserved at 1400° C. and 1000 Vcm⁻¹ in the pure-alumina samples.

The transition from a gradual enhancement in sintering rate to flashsintering seen in yttria-stabilized zirconia, with increasing field, isnot observed in MgO-alumina. In alumina the effect of field on thesintering rate is unremarkable below a threshold field. This thresholdfield is ˜500 Vcm⁻¹. Flash sintering is recorded at and above thisthreshold field.

The onset of flash sintering is accompanied with a non-linear increasein the conductivity of the specimen. This power surge was also seen inyttria-stabilized zirconia. However, an incubation time for this onsetis present in MgO-alumina which was not observed in yttria-stabilizedzirconia.

The conductivity of the alumina samples was measured in conventionallysintered, fully dense samples of alumina, independently of the sinteringexperiments. The non-linear increase in conductivity with applied fieldthat was seen during flash sintering was also present in these densesamples. The effect of doping was similarly reflected in thesemeasurements: the pure samples, which did not exhibit field assistedsintering also did not show non-linear behavior in conductivity.

The conductivity data for the pure samples remained Ohmic and wellbehaved over the full range of fields and temperatures in the presentstudy. All data conformed to approximately a single valued activationenergy, which was in the range of 170-225 kJmol⁻¹. These activationenergies are far too low for ionic diffusion. The inference is that theconductivity in the present experiments was dominated by electrons andholes. The easy and quick attainment of steady state current uponapplication of the electric field via platinum electrodes is alsoconsistent with the non-blocking nature of these electrodes forelectronic conduction.

The conductivity of the MgO-doped samples could be separated into tworegimes: below ˜200 Vcm⁻¹ the behavior remained linear. However, athigher field the currents increased in a highly non-linear fashion.Furthermore, when the field was cycled up and down, the current duringthe downward portion of the cycle was greater than when the field wasbeing increased. This hysteretic behavior became increasingly pronouncedas the amplitude of the applied field was increased. The cyclic behaviorwas fully reversible and linear when the amplitude was kept less than200 Vcm⁻¹.

The activation energy plots for conductivity in the MgO-doped samplesbore similarity with, but also differed from those for the pure samples.In pure-alumina the data for all fields and temperature conformed to asingle line on an Arrhenius plot. In the MgO-alumina, the data for asingle value of the applied field did fit an approximate straight line,but these lines shifted parallel to one another, and upwards to higherconductivities as the field was increased. Interestingly the slope ofthese lines, that is the activation energy, matched the value measuredfor the pure samples. It is inferred that activation energy for thediffusion of conducting species was left unchanged by the applied field,but the pre-exponential which is proportional to the concentration ofthe charge defects increased with the applied field in the dopedsamples.

The confluence of the onset of non-linear conductivity (in fully densesamples) and the onset of Flash sintering in field assisted sinteringexperiments is noteworthy. Normally, the conductivity and sintering ofceramics is controlled by different diffusion transport mechanisms. Theconductivity is determined by the fastest moving charge species, whilesintering is controlled by the transport of charge neutral moleculeswhose overall diffusivity is controlled by the slowest moving chargedspecies in the molecule. It follows, that the mechanism that is proposedfor the flash sintering phenomenon must explain this dichotomy betweentransport kinetics for charge conduction and sintering.

The nucleation of Frenkel pairs under the applied field is proposed as apossible mechanism to explain the above dichotomy. In this mechanism avacancy and an interstitial are created simultaneously for both thecations and the anions. The Frenkel pairs carry opposite charge relativeto the lattice, one carrying an electron and the other a hole. It isproposed that the electrons and the holes are separated from thesedefects under the applied field which renders the vacancies and theinterstitials to become charge neutral relative to the lattice therebyenhancing their mobility. The bias from the sintering pressure thenpulls the interstitials preferentially into the pores and the vacanciesinto the grain boundaries leading to densification. In this way theelectronic conductivity becomes coupled to the sintering kinetics.

The difference in the conductivity and sintering behavior of MgO-dopedalumina and alumina of nominal purity is highly remarkable, anddifficult to explain at this point. It is known that MgO has limitedsolubility in alumina, and that it segregates to the grain boundaries atrelatively low overall concentrations. At low applied fields the pureand MgO-alumina have very similar conductivities, and exhibit similarsintering kinetics. But at high fields the properties diverge with theMgO-alumina exhibiting flash sintering as well as non-linearconductivity, while the pure-alumina remains well behaved. The similarconductivity of the two aluminas at low field makes it unlikely that MgOis influencing the electronic conductivity of alumina—its effect appearsto be on the non-linear behavior. If the Frenkel defect nucleationmechanism were to hold, then its effect must be related to thisnucleation mechanism. One possibility is that the dopant creates localamplifications in the electrical fields which enhance the probabilityfor the nucleation of Frenkel pairs.

Example 3 Flash Sintering of SrTiO₃

Flash sintering of strontium titanate (SrTiO₃) was studied at differentapplied fields to understand its effect on density and grain growth. Inparticular, the defect structure was investigated by optical andstructural analysis. SrTiO₃ exhibited a trend in densification oppositethat of ionically or electronically conductive ceramics: as the appliedvoltage decreased, the density increased. Abnormal grain growth inconventionally sintered SrTiO₃ was arrested by flash sintering.Interestingly, undoped SrTiO₃ behaved differently than undoped Al₂O₃,which did not exhibit any signs of flash sintering. Previous attempts atflash sintering could only be achieved in MgO-doped Al₂O₃. It ispossible that non-stoichiometric Ruddlesden-Popper phases in SrTiO₃, asindicated by ultrafast optical spectroscopy, X-ray diffraction,conductivity measurements, and transmission electron microscopy,assisted flash sintering by increasing local conductivity throughenhanced defect content.

I. Introduction

Electric current-assisted sintering or simply Field-Assisted SinteringTechniques (FAST) have advantages, compared to conventional methods, ofreduced sintering time and temperature by adding an electric field tothe standard controls of time, temperature, and pressure. The most wellknown example is spark plasma sintering (SPS), which uses electricalheating of graphite dies along with uniaxial pressure. This widely usedsintering method has been demonstrated to give high density, small grainsize, and clean grain boundaries with enhanced sintering rates.

A novel electric current-assisted sintering method—flash sintering hassuperior time and temperature reduction without the need of highpressure unlike SPS. Flash sintering has been demonstrated to be aninnovative sintering method for ionic conducting and electronicconducting ceramics. Yttria-stabilized tetragonal zirconia and cobaltmanganese oxide spinel were successfully sintered at 850° C. and 325°C., respectively, in a few seconds under an applied DC electric field.To achieve dense compacts of these materials via conventional sinteringrequires temperatures greater than 1000° C. for several hours. Similarto other FAST sintering methods, flash sintering has producednanomaterials without any substantial grain growth compared to theoriginal powder. Flash sintering of SrTiO₃, a complex, undoped insulatoris reported herein. This work demonstrates that flash sintering can beused to sinter a wide range of ceramic materials. Microstructural aswell as optical characterization is performed to give insight into thedefect structure formed during flash sintering.

II. Experimental Procedure

Strontium titanium oxide, SrTiO₃ powder (Alfa-Aesar, Ward Hill, Mass.)with 99.9% purity was used as received. The powder has a specificsurface area of 20 m²/g, with an average particle size of 0.15 μm and adensity of 4.81 g/cm³. It is mixed with 5 wt % polyvinyl alcohol (mw49000; Fluka, Sigma Aldrich, Milwaukee, Wis.) in water to improve thegreen body strength. The amount of polymer was kept to a minimum toprevent contamination at the grain boundaries. Powder was uniaxiallypressed into a dog bone shape with a relative green density of 50%. Theprocess is explained in detail in a previous study. (M. Cologna, et al.,“Field Assisted and Flash Sintering of Alumina and its Relationship toConductivity and MgO-Doping,” J. Eur. Ceram. Soc., 31, 2827-37 (2011),incorporated herein by reference in its entirety).

The binder was completely removed after pre-heat treatment at 500° C.for 5 h with a rate of 2° C./min Sintering was performed in a verticalfurnace by suspending the samples by two platinum wires in the furnace.The voltage at the two electrodes was kept constant, while the furnacetemperature was increased from RT to 1400° C. with a heating rate of 10°C./min Once the sample reached the “flash sintering” regime, the heattreatment is stopped and the sample left in the furnace as it cooled.This regime can be considered as the densification stage of the samples.A conventionally sintered sample, sintered without any applied voltage(0 V), was prepared for comparison. It was sintered by one stepsintering, using the same furnace and conditions at 1400° C. for 1 h.

The dimensions of the suspended sample were recorded with a CCD camerathrough a silica window and a low pass filter (KG3 Shott), positioned inseries before the camera. The shrinkage strain is calculated as the truestrain, e=ln(l/l₀), where l is the time-dependent gage-length and l₀ isthe initial gage length.

(1) Characterization

Field emission scanning electron microscopy (FE-SEM) and a focused ionbeam/high resolution scanning electron microscope (FIB-SEM) were used toexamine the microstructure of the flash sintered and conventionalsintered samples. Microstructural studies on SrTiO₃ samples were done atthe University of Colorado, Boulder with a JSM-7401F FE-SEM (JEOL Ltd.,Akishima, Tokyo, Japan) and Los Alamos National Laboratory by FEI StrataDB235 FIB-SEM; FEI Company, Eindhoven, the Netherlands. Electronbackscatter diffraction (EBSD) was performed at 20 kV in an FEI XL30 SEMequipped with TSL/EDAX data acquisition software. The orientation datawere analyzed using TSL/EDAX OIMTM Analysis software. 0.2 μm step sizescans of areas 20 μm×20 μm were performed. Small area scans werepreferred due to charging of the sample. Several scans were run to covera greater area and obtain results representative of the entire sample.The number of analyzed grains was larger than 1000 for each sample.

Transmission electron microscopy (FEI Tecnai F30 analytical TEM; FEICompany, Eindhoven, the Netherlands) was applied to study themicrostructure. The images were recorded by a high-resolutioncharge-coupled device camera (Ultrascan 4000 4 k×4 k CCD camera; Gatan,Pleasanton, Calif.). X-ray Diffraction measurements were made on theRigaku Ultima III diffractometer that used a fine line sealed Cu tube togenerate Ka (k=1.5406 Å) X-rays. The generator was a D/MAX Ultima serieswith a maximum power of 3 kW. The bulk densities (ρ) of the samples weremeasured by Archimedes' method. The porosity of the samples wascalculated from the bulk density, using a value of 5.13 g/cm³ for fullydense SrTiO₃. Ultrafast optical spectroscopy measurements were performedin a pump-probe geometry and employed 50 fs laser pulses generated by anamplified Ti:Sapphire system at 250 kHz (Coherent RegA9500; CoherentInc., Santa Clara, Calif.). The pump pulses were centered at 266 nm (4.5eV) while probe pulses were tuned to 520 nm (2.4 eV). The pump beam ismodulated at 3 kHz by a mechanical chopper and a lock-in amplifier(Stanford Research Systems SR830, Sunnyvale, Calif.) was used to extracttransient reflectivity changes from the probe signal. The pump beamfluence was kept at ˜0.1 mJ/cm², while the probe beam fluence was fixedat ˜0.1 lJ/cm². All measurements were performed at room temperature(T=295 K). Finally, conductivity measurements were done in two-pointcontact mode on flash sintered and conventional sintered SrTiO₃. Theconductivity of sintered specimens is measured in cyclically appliedelectrical fields of various amplitudes and details are given elsewhere.(M. Cologna, et al., “Field Assisted and Flash Sintering of Alumina andits Relationship to Conductivity and MgO-Doping,” J. Eur. Ceram. Soc.,31, 2827-37 (2011), incorporated herein by reference in its entirety).

III. Results and Discussion

(1) Flash Sintering and Microstructural Changes

Sintering curves of the flash sintered SrTiO₃ at three differentvoltages are in FIG. 16. For an applied voltage of 1000 V/cm, flashsintering conditions were achieved at 740° C. with the sinteringoccurring in just a few seconds. The sintering process was hindered dueto the limitation of the maximum current, which was kept at 60 mA (max.power 120 W). The density of this sample (<70%) was found to be too lowfor additional study. To improve the density, the maximum current waskept the same while the voltage was decreased to 500 V/cm. Under theseconditions, flash sintering occurred at 900° C. with a final linearshrinkage of 27%. The decrease in voltage caused the sinteringtemperature to increase from 740° C. to 900° C. Final grain size wasexamined by SEM in FIG. 17. It retained the starting 150 nm powder size,while the density increased to 76% of the theoretical density. Thisresult demonstrates the reverse relationship between voltage andsintering temperature as well as the relationship between thesevariables and sintered density.

The sintering conditions were optimized—highest densities and smallestgrain sizes—when the voltage was fixed to 150 V/cm and the maximumcurrent was increased to 500 mA. Flash sintering conditions is achievedat around 1200° C. with a significant grain growth, as shown in FIG. 18.The average grain size is around 1 μm while the density was greater than95% of theoretical density. The estimated density based on the shrinkagewas 4.75 g/cm³, which agrees well with our measured density. Thesintering rate at this voltage was lower than for the other sinteringconditions examined. The sudden grain growth and lower sintering ratessuggest that the sintering conditions tend to change from the flashsintering to the FAST sintering regime. Note that flash sinteringdescribes an instantaneous sintering, whereas FAST sintering is agradual increase in shrinkage rate.

Arrhenius plots of power-dissipation were reported in FIG. 19. A suddenpower surge, characteristic of flash sintering, occurred above 5 W at1000 and 500 V/cm. This critical power dissipation level was slightlyhigher at 150 V/cm, which confirmed the transition from flash to FASTsintering. Finally, the power dissipation level observed here was thehighest reported value among all previous studies, which was likely dueto the relatively high resistivity of SrTiO₃; it is known that the fieldrequired for flash sintering decreases as conductivity increases.

Conventional sintering was done at 1400° C. for 1 h of soaking time togather further insight into the flash sintering process. The averagegrain size for the conventionally sintered material was found to be 1.5μm with a high grain size gradient across the sample (FIG. 20). Thefinal density obtained was only 92% of theoretical density. Density andparticle size changed with respect to furnace temperature as shown inFIG. 21. The applied voltage was given as a dashed line to reveal itseffect on the other parameters. Particle size remained constant until900° C. with 500 V/cm applied field and increased linearly afterward.Similar behavior was reported for spark plasma sintering where the grainsize remained constant until a critical temperature is reached. Thiscritical temperature for SrTiO₃ should be higher than 900° C. sincegrain size increased abruptly after this temperature. On the other hand,this temperature can be controlled and, most significantly, reduced byan applied voltage; higher voltages gave lower sintering temperatures.

Electron backscatter diffraction was performed to explore the possibletexture formation due to electrical field usage in flash sintering andto characterize the grain boundary structure of flash sintered andconventionally sintered SrTiO₃. Due to the non-conductive nature ofSrTiO₃, several small area scans (about 20 lm 9 20 lm) were done oncarbon-coated samples (thickness of 30-50 nm) along the sample normaldirection. Orientation image maps (OIMs) obtained on SrTiO₃ samplessintered at 150 and 0 V/cm (conventional sintering) were given in FIGS.22A and 23A, respectively. Each of the image maps of these figures wasthen converted into a size histogram. The average grain size for flashsintered SrTiO₃[FIG. 22A] is 0.9-1 μm, with a small outlying population(0.2% area fraction) of larger grains with sizes of 1.2-1.4 μm. FIG. 23Bshows a similar histogram for conventionally sintered SrTiO₃, but withwider grain size distribution (1.7-3 μm). With increasing sintering timeand temperature, the fraction of large grains increased, as did theiraverage size. The EBSD and FE-SEM results are evidence that flashsintering acts to stop abnormal grain growth, which is observed to agreater degree in conventionally sintered SrTiO₃.

In previous work, it was demonstrated that both the average grain sizeand density increase with increasing applied voltage inyttria-stabilized zirconia (YSZ), which is the opposite trend observedhere for SrTiO₃. This may suggest that the flash-sintering mechanism innon-conductive ceramics is different than in ionically or electronicallyconductive ceramics (YSZ, Co₂MnO₄, etc.). An additional decrease involtage from 150 V/cm to 0 V did not improve the density but rather leadto a decrease in density. The density of conventionally sintered SrTiO₃at 1400° C. was 5% lower than the sample flash/FAST sintered at 1200° C.This shows that density can be improved and grain size refined at lowertemperatures by flash sintering even in non-conductive ceramics.

(2) Defect Structure Analysis

Although it has been demonstrated that flash and FAST sintering methods(i.e., spark plasma sintering) have advantages over conventionalsintering by decreasing temperature and time, the defect chemistry inthese systems is not understood completely. Flash sintering, occurringin only a few seconds under an applied electrical field is a complexprocess, resulting in extra difficulties in understanding the resultingdefect structure completely. The following section is an initialinvestigation into the defect structure of flash sintered SrTiO₃.

Optical characterization methods are very effective for analyzing defectstates in the material, especially sensitive to even small numbers ofdefects. In this work, we used ultrafast optical spectroscopy, which isvery sensitive to defect states and changes in bonding structure, tostudy the defect states in SrTiO₃. FIG. 24 shows the photoinducedreflectivity dynamics DR/R of conventionally sintered (0 V) andflash-sintered (150 V/cm) SrTiO₃ as a function of time delay betweenpump and probe pulses. The general feature of the dynamics observed inthe different samples was the fast (˜100 ps) relaxation of photo-inducedchanges back to the equilibrium value. This can be attributed toelectron-phonon scattering with subsequent electron-hole recombinationand lattice relaxation processes. In single-crystal SrTiO₃ (MTIcorporation, Richmond, Calif.) electron-hole recombination is slow(>1000 ps). The difference between the sintered and the single crystalresponse suggests that this is a direct consequence of a finite residualdefect concentration remaining due to sintering and or distortions,which can also act as defects in terms of their effect on thereflectivity dynamics. These defects were charge traps or scatteringcenters, providing additional routes for charge-lattice relaxation inthe crystal structure. The fact that the relaxation in both flash andconventionally sintered polycrystals occurred on almost the sametimescale indicates that the photoinduced reflectivity dynamics of bothsamples is very similar. The difference in signal amplitudes, however,might be related to gradients in grain size that causes scattering.

There were three primary possibilities for the source of the enhancedelectron-hole recombination: impurities, secondary phases, or pointdefects within the SrTiO₃ structure. The possibility of impurity contentcoming from the sintering process (specifically the binder) wasinvestigated using particle induced X-ray emission (PIXE). No impuritieswere detected (<10 ppm) within the sample, ruling out the firstpossibility. Sintered samples as well as the starting powder, forcomparison, were analyzed by XRD. All samples were cubic SrTiO₃ in thePm3m structure with a small shift in FIG. 25A, which is highlighted inFIG. 25B, where the most intense (110) peak is shown. The peak for thestarting powder, centered at 32.4°, shifts to higher 2Θ values in boththe sintered samples, indicating that the lattice parameter is becomingsmaller upon sintering. The starting powder had lattice constant ofa=3.905 Å (JCPDS#73-0661) while the sintered samples have smallerlattice constants (around 3.89 Å), an effect that is slightly greater inthe conventionally sintered sample than that in the flash sinteredsample. These shifts are attributed to distortions in the structure dueto sintering, which is consistent with the ultrafast opticalspectroscopy results. Such distortions in the structure can be caused bydefects (such as oxygen vacancies) or local non-stoichiometric phases,both of which can cause a radical difference in optical response of thematerial.

The TEM analysis of the microstructure was performed to understand thetype of defect structure which might be responsible for the peak shiftin the XRD and the changes observed in the reflectivity dynamics. As forthe XRD results, microstructure analyses by means of High ResolutionTransmission Electron Microscopy (HRTEM) imaging and micro-beam electrondiffraction patterns (MBEDP) indicated that sintered material has astoichiometric SrTiO₃ cubic structure (Pm-3m). However, some of thegrains have defect structures with irregularly spaced line features, asshown in the HRTEM image in FIG. 26. These defects are explained bylocal chemical deviations from stoichiometric SrTiO₃ and are referred toas Ruddlesden-Popper (RP) phases [SrO(SrTiO₃)n or Srn+1TinO3n+1]. Theyare introduced by the accommodation of long-range order latticedistortion and explained by self-healing of vacancy distortion byinsertion of shear planes. During sintering, structure can changesignificantly by reduction or oxidation at elevated temperatures.Structural distortions in stoichiometric SrTiO₃ under an appliedelectric field have been reported and explained by the ordering ofoxygen vacancies and electro-migration of SrO ion complexes. (D. C.Meyer, et al., “An Electrical Field-Induced Structural Effect inStrontium Titanate at Room Temperature,” Appl. Phys. A, 80, 515-22(2005) incorporated herein by reference in its entirety). Indeed, it hasbeen reported that RP phases cause the existence of RP phases induce ashift to the right in the positions of XRD peaks as n gets smaller. Thisis consistent with our XRD results. The initial powder is stoichiometricSrTiO₃ with n=∞; as non-stoichiometric RP phases are formed in thematerial, the average value of n decreases.

Finally, conductivity measurements are shown in FIG. 27. The temperaturedependence of the electrical conductivity (r) of SrTiO₃ samples followedan Arrhenius law. The activation energy values for flash sintered andconventional sintered SrTiO₃ agree well with literature values forSrTiO₃. On the other hand, both flash and conventional sintered SrTiO₃exhibit higher absolute conductivities compared to the literaturevalues. This difference in the conductivity is within the range of theexperimental error but can also be electrical conductivity (r) of SrTiO₃samples follows an Arrhenius law. The activation energy values for flashsintered and conventional sintered SrTiO₃ agree well with literaturevalues for SrTiO₃. On the other hand, both flash and conventionalsintered SrTiO₃ exhibit higher absolute conductivities compared to theliterature values. This difference in the conductivity is within therange of the experimental error but can also be caused by differences instoichiometry. It is known that the conductivity of SrTiO₃ can changeeasily with even small compositional changes such as oxygen deficiency,slight change in the Sr/Ti ratio or formation of Ruddlesden-Popperphases. Together, the optical spectroscopy, XRD, PIXE, conductivitymeasurements, and TEM revealed that sintering, either conventionally orflash, results in non-stoichiometric phases. The defect states detectedby optical spectroscopy and by the peak shift in the XRD are due todistortions in the cubic structure as a consequence of the formation ofRP phases.

In a previous work, we reported that undoped Al₂O₃ did not show anyflash sintering phenomenon; flash sintering could only be achieved upondoping with MgO. In the case of flash-sintered SrTiO₃, we believe thatnon-stoichiometry in the form of RP phases, enhances the sinteringprocess via an enhancement of conductivity which is particularlyimportant for the flash sintering process. Clearly, the defect structureof the material is important for the propensity for flash sintering tooccur. Although the flash sintered and conventional sintered sampleshave some qualitative similarities, the flash-sintered material has anoverall lower defect content, as determined by optical analysis and XRD.Thus, the differences are in number rather than kind.

IV. Conclusion

Strontium titanium oxide was flash sintered at different applied fieldsto understand the role of the field strength on density and graingrowth. The density increased with decreasing applied voltages, which isin contrast with the trend observed in ionically or electronicallyconductive ceramics (YSZ, Co₂MnO₄, etc.). The highest density material(more than 95%) is obtained for fields of 150 V/cm. At this appliedvoltage, flash sintering occurred at 1200° C. The density ofconventionally sintered SrTiO₃ at 1400° C. is 5% lower than that in thissample. Grain growth followed a similar trend as density and abnormalgrain growth, observed in conventional sintered sample, is arrested byflash sintering.

Optical and structural characterization reveals that sintering, eitherconventional or flash, induced the formation of non-stoichiometricphases in SrTiO₃. We believe that these defects assisted the occurrenceof flash sintering in pure SrTiO₃ as flash sintering did not occur inundoped Al₂O₃. Indeed, flash sintering was only achieved in Al₂O₃ upondoping with MgO. It is suggested that the non-stoichiometric RP phasesplay an important role in the processes associated with the flashsintering of SrTiO₃.

Example 4 Flash Sinterforging

The influence of a uniaxial applied stress on flash-sintering and fieldassisted superplastic behavior of cylindrical powder preforms of 3 mol %tetragonal-stabilized zirconia is reported below. The experiments used asinterforging method, where, in addition to pressure, a dc electricalfield is applied by metal electrodes sandwiched between the push-rodsand the specimen. The axial and radial strains in the experimentprovided simultaneous measurement of the time-dependent densificationand shear strains. Large effects of the electric field on sintering andsuperplasticity were observed. Flash-sintering was observed, which ischaracterized by a threshold level of temperature and electric field.With higher applied fields, the sample sintered at a lower furnacetemperature. Surprisingly, the applied stress further lowered thiscritical temperature: a sample, which sintered at 915° C. under a stressof 1.5 MPa, densified at only 850° C. when the stress was raised to 12MPa. This stress induced reduction in sintering temperature mayberelated to the additional electrical fields generated within thespecimen by the electro-chemomechanical mechanism described by Pannikkatand Raj [Acta Mater., 47 (1999) 3423], incorporated herein by referencein its entirety. The sample also deformed in pure shear to 30% strain injust a few seconds at anomalously low temperatures. The specimentemperature was measured with a pyrometer, during the flash sintering,as a check on Joule heating. A reading of 1000° C.-1100° C. wasobtained, up to 200° above the furnace temperature. This temperature isstill too low to explain the sintering in just a few seconds. While notwishing to be bound by theory, it is suggested that the electric fieldcan nucleate a defect avalanche that enhances diffusion kinetics not bychanging the activation energy but by increasing the pre-exponentialfactor for the diffusion coefficient, noting that the pre-exponentialfactor depends on concentration of defects, and not upon their mobility.

I. Introduction

Ceramics are almost always fabricated by a solid state sinteringprocess. In “free” sintering a preform shrinks into a self-similarshape. In hot-pressing and sinterforging experiments, the applied stresscauses not only a change in shape but also an increase in density.

The advantage of the sinterforging method is that both the axial and theradial strain in the specimen can be measured independently. These twostrains can then be combined to calculate two scalar quantities, thevolumetric strain, which equals densification, and shear strain, whichmeasures the change in shape.

The application of electrical fields greatly enhances sintering.Collectively, methods employing the use of an electric field have cometo be known as field assisted sintering techniques. The most commonmethod is spark-plasma-sintering (SPS), where, like hot-pressing, thepowder is densified in a graphite die under uniaxial pressure. Thedifference is that in SPS the graphite die is heated directly byelectrical current, which can be in the range of several kilo Amperes.The uniaxial pressure is applied by a hydraulic mechanism. While thereis clear evidence that sintering of ceramics is greatly enhanced in SPS,the underlying mechanisms remain elusive because it is often difficultto separate the current flowing through the die from the current flowingthrough the powder compact. Since SPS is often carried out under bothpressure and electrical current, it has been difficult to study howthese two parameters individually influence the sintering behavior,especially because the magnitude and the wave shape of the electricalcurrent is constrained by the heating schedule of the graphite die,rather than by the intrinsic need to study field assisted sintering ofceramics.

To better understand the role of electrical fields on the sinteringprocess, experiments where samples were heated within a conventionalfurnace while the electrical fields are applied independently to thespecimen are being carried out. Since the voltage was applied by meansof two electrodes to the specimen, this has been named the two electrodemethod. These experiments have shown that when the applied field exceedsa critical value, ceramics sintered in just a few seconds at anomalouslylow temperatures—a process called flash sintering. In a typicalexperiment, a constant potential difference is applied across thespecimen while the sample is heated at a constant rate. The samplesinters abruptly to nearly full density above a threshold temperature.When the experiment is repeated at a higher applied field, thetemperature for the onset of flash sintering is lowered. In the case ofyttria-stabilized zirconia, we observed two regimes of behavior. At highfields the sample sintered abruptly by flash sintering; at lower fieldsthere was a gradual increase in the sintering rate. The latter processhas been successfully explained by a slower rate of grain growth underan applied field, but the underlying mechanism for flash sinteringremains elusive.

Field assisted sinterforging is an effective way to expose theunderlying science of SPS. The experimental arrangement is sketched inFIG. 28. The stress was applied uniaxially without a lateral constraintto the specimen. The furnace temperature, the field applied to thespecimen, and the uniaxial stress can now be controlled independently ofone another.

The field assisted sinterforging experiments, reported here, werecarried out on the same ceramic powder of 3YSZ as in the earlierflash-sintering experiments. (M. Cologna, et al., “Flash Sintering ofNanograM Zirconia in <5 s at 850° C.,” J. Am. Ceram. Soc., 3559, 3556-9(2010), incorporated herein by reference in its entirety). We hadexpected that the stress would enhance the rate of sintering. Instead,rather surprisingly, we find that the applied stress acted like theelectric field, lowering the threshold temperature for the onset of theflash effect.

Sinterforging experiments provide data on shear deformation as well asdensification. Both phenomena require mass transport to and frominterfaces. In sintering, mass is transported from grain boundaries tothe adjacent pores. In shear deformation, or superplasticity, mass movesfrom interfaces in compression, to those in tension, producing a changein shape. Present experiments show that electrical fields can accelerateboth sintering as well as superplasticity, implying that electricalfields have a fundamental influence on mass transport. We reportfield-assisted superplastic strain rates of up to 0.09 s⁻¹ attemperatures as low as 850° C. These deformation temperatures areseveral hundred degrees lower than those required in conventionalsuperplasticity. To some extent these higher deformation rates are aconsequence of the samples being porous, but this argument cannotexplain the dramatically lower temperatures of deformation, even afterallowing for Joule heating which accompanies “flash” sintering andsuperplasticity.

Indeed, one of the objectives of these studies was to ask the questionwhether the flash phenomenon is simply a result of Joule heating, orwhether there was a different mechanism at play. Measurement of thespecimen temperature with a pyrometer during flash sintering shows thatJoule heating alone cannot explain these enormously fast rates ofsintering and deformation. We propose a mechanism, which is likely to becontroversial, that electric fields induce a defect avalanche whichgreatly increases the pre-exponential in the diffusion coefficient. Thismechanism does explain the rather unusual coupling between theelectronic current which requires transport of charge, and chemicaldiffusion which is necessary for sintering and superplasticity. Chemicaldiffusion is controlled by charge neutral transport of mass, that is, bythe slowest moving charged species, while the fastest moving speciesdetermines the electronic current.

II. Experimental Methods

(1) Sample Preparation

Tetragonal Zirconia, doped with 3 mol % Yttria, was pressed intocylindrical compacts by cold pressing in a steel die at 35 MPa. Theaverage particle size, given by the manufacturer (Tosoh USA, Grove City,Ohio), was 60-70 nm. The compacts were pre-sintered by heating from roomtemperature to 850° C., using a ramp rate of 1.5° C./min, and holding atthat temperature for 4 h. The green density of these slightlypresintered specimens was in the 50%-55% range. This procedureaccomplished two tasks: it removed the binder, and produced some bondingbetween the particles, which enabled the preform to withstand theapplied load in sinterforging experiments. These cylindrically shapedpowder compacts were 5 mm in diameter and 10 mm in height.

(2) Sinterforging Experiments

The experiment is sketched in FIG. 28. The arrangement is similar to thesetup used by 7K. R. Venkatachari and R. Raj, “Shear Deformation andDensification of Powder Compacts,” J. Am. Ceram. Soc., 69, 499-506(1986), incorporated herein by reference in its entirety, with twonotable differences: the axial load was applied using a pneumaticcylinder rather than with a traveling crosshead, and the radial andaxial strains were obtained by analyzing the images, obtained with acamera through optical filters, at intervals of 1 s, rather than withLVDTs. The experiments were performed in a modified box furnace (CMFurnaces, Bloomfield, N.J.) that operates in ambient air, withmolybdenum-discilicide heating elements. All experiments were carriedout at a constant heating rate of 10° C./min.

The electrical field was applied with electrodes made from sheets ofstainless steel, placed in between the alumina pushrods and the two flatfaces of the specimen. Each experiment was performed at a constantvoltage from a dc power source (Sorenson DLM-300; Sorensen, San Diego,Calif.). The current flowing through the specimen was measured usingdigital multimeter (KeithleyModel 2000; Keithley, Cleveland, Ohio). Thepower source was set to limit the current to prevent runaway heating ofthe specimen; this point is further discussed later.

The experiments were carried out in the following way. The greencompacts were placed between the stainless steel electrodes and thealumina push rods. The load was raised to the desired sinter-forgingpressure, using the initial dimensions of the specimen, and then heldconstant throughout the experiment. The voltage was set to a givenvalue; the electric field values quoted in the figures refer to theinitial length of the specimen. Once the voltage and pressure werestable the furnace was set to heat from room temperature at a rate of10° C./min The measurements of the radial and the axial strains weremade using a camera taking snapshots at 1 s intervals. The flash eventwas accompanied by an abrupt increase in the current, which we havecalled a power surge. The current was allowed to rise until a presetcutoff was reached. At this point, the power controller switchedautomatically to a current controlled mode; this led to a decline in thevoltage, and thus to a reduction in the power (=voltage 9 current),applied to the sample, since the conductivity of the specimen continuedto increase despite reduced power dissipation. This lag between powerdissipation and the increase in conductivity is a noteworthy observationfrom these experiments. Upon completion of flash sintering, the power tothe specimen was disconnected. At the same time, the furnace was turnedoff, and the specimen was allowed cool at a rate of 30° C./min down toroom temperature.

(3) Equations for Data Analysis

The axial and radial strains in the specimen were measured from thedigital photographs. If the time dependent axial length of the sample isL(t) and its radius is R(t) then the axial and radial (true) strains aregiven by:

$\begin{matrix}{ɛ_{z} = {\ln \left( \frac{L}{L_{0}} \right)}} & (1) \\{ɛ_{R} = {\ln \left( \frac{R}{R_{0}} \right)}} & (2)\end{matrix}$

where, L₀ is the initial length and R₀ is the initial radius of thespecimen. The shear, or deviatoric strain, ∈_(e), and the volumetricstrain, ∈_(a), both scalar quantities, are then obtained from thefollowing equations:

$\begin{matrix}{ɛ_{e} = {\frac{2}{3}{{ɛ_{z} - ɛ_{R}}}}} & (3) \\{ɛ_{a} = {{{ɛ_{z} + {2ɛ_{R}}}} = {\ln \left( \frac{\rho}{\rho_{g}} \right)}}} & (4)\end{matrix}$

Note that |∈_(a)| is related to the initial green density, ρ_(g), and tothe time dependent density, ρ(t), as shown on the right in Eq. (4).Therefore, the time-dependent density of the sample can be calculated bymeasuring the volumetric strain and substituting into Eq. (4).

III. Results

(1) Constant Applied Field (100 V/cm), Variable Load (1.5-12 MPa)Experiments

The data were plotted with furnace temperature along the horizontal axis(this is synonymous with time since the experiments were carried out ata constant heating rate of 10° C./min). Six different experiments werecarried out at applied stresses ranging from 1.5 to 12 MPa, all at afield of 100 V/cm. The measurements of the axial and radial strains wereconverted into volumetric and shear strains with Eqs. (3) and (4). Theresults are given in FIGS. 29 through 32. The following features arenoteworthy:

Like flash sintering, the sinterforging experiments exhibited an abruptonset of axial and radial strains above a threshold temperature.However, the threshold temperature was stress dependent. At 1.5 MPa, thetransition temperature was 910° C. As the stress is increased thistemperature continued to fall, reaching down to 850° C. at 12 MPa.

In FIG. 29, we noted that the axial as well as the radial strainremained negative, showing that the specimen continued to shrink involume. In free sintering, the axial and radial strains would have beenequal to one another, consistent with a self-similar change indimensions. Here, however, these strains were unequal, the differencebetween them being a measure of the shear strain, embodied in Eq. 3.This difference increases with the applied stress consistent with theclassical behavior of stress-dependent creep.

FIG. 30 gives plots for the densification strains as calculated from Eq.(4). Note that the densification strain saturated at the same value, of˜0.6, at all stress levels. This is because densification stopped whenthe specimen reached full density. The experimental value of the finaldensity of the specimens was between 95% and 98%. Substituting thesevalues into Eq. (4), and setting ea |∈_(a)|=0:6, produced a greendensity ρ_(g)=0.52-0.53, in good agreement with the experimental range.

FIG. 31 gives plots of the sintering rates on an expandedtime-temperature scale. These graphs were derived from the same datathat were used for FIG. 30. The plots in FIG. 31 give an idea for (i)the duration of flash sintering, and (ii) the influence of the appliedload on the maximum sintering rate. In all instances, the sintering rateincreased abruptly as the flash temperature was crossed, and then fellquickly to zero as full densification was achieved. The time scale,given alongside the temperature scale (the heating rate was equal to 10°C./min), showed that sintering was completed in about 10 s. It isparticularly significant that the rates of sintering were independent ofthe applied stress. Instead the applied stress had the effect oflowering the temperature for the onset of flash-sintering.

FIG. 32 gives plots for the shear strain as calculated from Eq. (3).Unlike densification, the shear strains continued to increase withapplied stress (this is not related to temperature since thetemperatures are lower for the higher strains). In sinterforgingexperiments, the specimens were not constrained and therefore couldcontinue to deform in shear. The important finding here was that underthe “flash” conditions the specimen could not only densify but alsodeform at unusually low temperatures. The true strain of 30% achieved ina few seconds at 12 MPa and ˜850° C. was quite remarkable and isreferred to as field assisted superplasticity, herein.

(2) Constant Load, Variable Field (0-200 V/cm) Experiments

In these experiments, the applied load was held constant at 5 MPa, whilethe field was increased from 0 to 200 V/cm. Plots of densificationstrain and shear strain are given in FIG. 33. It is interesting tocompare the graphs for the shear strain in FIGS. 32 and 33. When theexperiments were carried out at increasing load (at a constant field),as in FIG. 32, the shear strain increased with the applied stress.However, if the field was increased while holding the load constant, theshear strain remained unchanged. This result provides insights into therole of the field and the stress in field-assisted superplasticity.Applied stress provides the driving force for superplastic deformation;thus the magnitude of the strain increases with the applied stress. Theelectrical field, apparently, does not contribute to the driving force,since the magnitude of the shear strain is independent of the electricfield. The inference is that the field increases the rate of masstransport, not the essential driving force for superplastic deformation.

(3) The Correlation Between Flash-Sintering and the Power Surge

Flash sintering appears, always, to be accompanied by a power surge,identified by a sudden increase in sample conductivity. In thesemeasurements, the power dissipated in the specimen is calculated as theproduct of the applied voltage, which is held constant, and the current,which increases abruptly. Therefore, the abrupt increase in power wasdirectly proportional to the sudden increase in the electronicconductivity. The plots for the power dissipated in the specimens at anapplied field of 100 V/cm, at different values of the applied stress aregiven in FIG. 34. The power was normalized with respect to the volume ofthe specimen, which in the green state was equal to 196 mm³.Interestingly, for reasons that are not clear, the cusp of the powersurge appears to occur at the same level of power, ˜20 mW/mm³, whichcorresponds to 4 W of actual power dissipated in the specimen. The powerdissipation increases abruptly beyond this point, reaching up to nearly100 W before the current limit in the power supply comes into play.

The strong correlation between the power-surge and flash sintering isshown in FIG. 35, where data for different applied stresses, at aconstant field of 100 V/cm, have been plotted. The plots for the powerwere shown in dotted lines, with the scale given on the left. Thedensification strain was plotted in triangles linked by solid lines,with the scale shown on the right. The maximum point in the power arosefrom the manner of the experiment. The power dissipation rose since thepower supply was voltage controlled: as the current through the specimenrose, so did the power. However, the power supply was programmed toswitch to current control when a limit of 1.0 A was reached. Thereafter,the voltage in the specimen dropped since its conductivity continued toincrease, even though the current through the specimen was limited.Power dissipation in the specimen, therefore, dropped since it was equalto the product of the current (a constant) and the voltage (declining)It was noteworthy that the conductivity of the specimen continues toincrease even when the power dissipation has crossed the peak.

FIG. 35 also shows that densification was coupled to the increase in theconductivity of the specimen. Like the change in conductivity, thedensification curve lagged the power surge by a noticeable shift to theright. This lag can be explained in two ways: (i) it may be related to adelay in the temperature rise of the specimen because of the transientnature of Joule heating in the specimen; or (ii) it is also possiblethat the onset of flash sintering resembles a nucleation event, carryingan incubation time before it is activated. Arguments can be made forboth suggestions. While the thermal transient argument is certainlyviable, we slightly favor the nucleation mechanism since the onset offlash sintering occurred not during the rising part of the powerdissipation curve but instead when the power is declining We pose thisdilemma as a question for future work, urging the reader to not assumethat the flash sintering effect is solely a consequence of Jouleheating.

(4) Measurement of the Specimen Temperature

The correlation between the power surge and densification raises thequestion of Joule heating. This issue was addressed by measuring thetemperature of the specimen with a pyrometer through the same window inthe furnace that was employed for the camera. (Consequently, it was notpossible to measure the strain and the temperature of the specimenconcurrently. However, this was not consequential since the correlationbetween the power surge and densification has been clearly establishedin FIG. 35.)

The results from an experiment run at 5 MPa and 100 V/cm are given inFIG. 36. The power dissipation is plotted using the dotted line. Itconsists of two regimes. In the first regime, marked as A, the powersupply was operated under voltage control: as the current rose so didpower dissipation. Once the current limit set in the power supply wasreached, the power supply became current controlled leading to regime B.As the conductivity of the specimen continued to increase, the voltagedeclined and so did the power dissipation (since power is the product ofvoltage and current). Eventually the electric field to the specimen aswell as the furnace was turned off as shown by the downward arrow.

The measurements from the pyrometer are shown on the same graph with thetemperature scale given on the right. At first, the pyrometer trackedthe furnace temperature as pointed out by the straight line explained inthe bottom right of the figure. But as the power dissipation increased,the specimen temperature moved higher but shifted slightly to the rightand mostly in the B-regime where the power to the specimen wasdeclining. Below we show a good correlation between the densificationcurve and the shape of the temperature data measured with the pyrometer.

An expanded view of the power and the densification data, highlightingtheir interdependence was given in FIG. 37 (this is the same data asgiven in FIG. 35). It clearly shows that densification occurred notduring the rise in the power dissipation but rather during thecurrent-limited regime-B where the power dissipation was declining. Thepyrometer data, from FIG. 36, drawn to scale, are included as a faintline in this plot to highlight the lag between specimen temperature andthe power surge. These coordinated plots suggest that densificationfollows the rise in specimen temperature, not the rise in powerdissipation. Both densification and the specimen temperature slightlylag power dissipation. It is especially noteworthy that densification iscompleted when the specimen temperature, as measured with the pyrometer,is about midway between 1000° C. and 1100° C.

Thus, it has been inferred that the specimen reaches full density whenits temperature is below 1100° C. This temperature range is far too lowfor conventional sintering in just a few seconds (without an appliedfield). Thus, it would appear that flash sintering is not a result ofJoule heating, although the surge in specimen conductivity and flashsintering occur together. The question is to identify a mechanism thatcan simultaneously explain the sudden increase in conductivity as wellas the sintering rate. Keep in mind that while the conductivity dependson the transport of electrons, sintering is controlled by transport ofcharge neutral molecules.

(5) Field Assisted Superplasticity

The results in FIG. 32 conclusively show that the application ofelectric field produced high rate superplasticity in 3% yttria-dopedzirconia. Here, the data for shear deformation is analyzed in terms ofthe classical equation, in an attempt to elicit how the applied fieldaffects the key parameters for superplastic deformation, namely, thestress exponent, the activation energy, and the pre-exponential for thecoefficient of self-diffusion.

Superplastic deformation in ceramics is described by the followingequation:

$\begin{matrix}{{\overset{.}{ɛ}}_{e} = {\frac{B}{d^{3}}\sigma_{e}^{n}D_{0}^{- \frac{Q}{RT}}}} & (5)\end{matrix}$

where ∈_(e) is the deviatoric or shear strain rate, B is a constant,which includes the effect of the relative density of the specimen, d isthe grain size, σ_(e) is the deviatoric or the effective shear stress, nis the stress exponent, D₀ is the pre-exponential for the diffusioncoefficient, Q is the activation energy for self-diffusion, T is thespecimen temperature in Kelvin, and R is the Gas constant. The stressexponent, ideally, is predicted to be equal to n=1 for the case ofdiffusional creep.

Equation (5) gives an opportunity to explore how the electric field caninfluence the stress exponent, the activation energy and thepre-exponential for diffusion, D₀ in the equation for superplasticdeformation. The data for application to Eq. (5) are summarized in Table2.

TABLE 2 Values for the Parameters in Eq. (5) Used to Elicit Values forthe Stress Exponent and the Activation Energy Specimen Applied stressMax. shear Relative Furnace temp. (MPa) strain rate (s⁻¹) density temp.(° C.) (Est) (° C.) 1.5 0.04 0.87 916 1083 3 0.06 0.8 895 1071 5 0.080.79 876 1061 7.5 0.09 0.88 866 1056 9 0.09 0.8 858 1052 12 0.09 0.83850 1048

The six values of the applied stress are listed in the left column. Themeasured values of the maximum shear strain rate and the relativedensity where this occurs are given in the next two columns. Thefollowing column gives the furnace temperature. The grain size may beassumed to have been constant since the shear strains were measured atdensities that were low enough to retain open porosity, a conditionunder which there is little grain growth. The question now arises aboutestimating the specimen temperature under the transient conditionsexperienced in the experiment.

We attempt to estimate the specimen temperature from the equationderived on the basis of a balance between power dissipation and blackbody radiation:

$\begin{matrix}{\frac{\Delta \; T}{T_{0}} = \frac{\Delta \; W}{4A\; \sigma \; T_{0}^{4}}} & (6)\end{matrix}$

Here, ΔT is the increase in specimen temperature relative to the furnacetemperature T₀ (in Kelvin), when power ΔW watts is expended in thespecimen. The Stefan-Boltzmann constant is σ=5.67×10⁻⁸W·m²·K⁻⁴representing a physical constant. The approximate nature of the analysisis quite apparent. A considerable fraction of the power expended in thespecimen is likely to have been drawn away by conduction into thealumina push rods that are in contact with the specimen through thestainless steel electrodes. Therefore, a direct insertion of watts asmeasured from the power supply, into Eq. (6) is likely to overestimatethe specimen temperature. Nevertheless, black body radiation will beimportant in the overall thermal problem, and the inverse dependence onthe fourth power of the furnace temperature in Eq. (6) could be quiteimportant in influencing the specimen temperature. A reverse calculationshows that ΔW=10 W gives a reasonable agreement between the estimatefrom Eq. (6) and the specimen temperature measured with the pyrometer.The specimen had an exposed surface area of 1.69 10⁻⁴ m². If T₀, thefurnace temperature is 875° C., then substituting these values into Eq.(6) gives ΔT=193 K, that is, a specimen temperature of 875+193=1068° C.is estimated, in good agreement with the pyrometer reading of ˜1075° C.This procedure leads to estimates of specimen temperatures listed in theright hand column in Table 2. There is surely an error in theseestimates but, as explained above, the error is systematic and thereforeshould yield plausible trends in the behavior. Since the estimate of theactivation energy depends on how rate changes with a change intemperature, the procedure given below is expected to yield reasonablycredible values for the activation energy.

The values in Table 2 may be used to obtain a value for n and Q byrewriting Eq. (5) in the following way:

$\begin{matrix}{{\log_{10}\left( \frac{{\overset{.}{ɛ}}_{e}}{\sigma_{e}^{n}} \right)} = {{\frac{- Q}{2.3R} \cdot \frac{1000}{T\left( {\Delta \; W} \right)}} + A}} & (7)\end{matrix}$

Here, Q is written in units of kJ/mol, and the constant contains thetemperature independent variables in Eq. (5). An Arrhenius plot for Eq.(7) is given in FIG. 38, for the case n=1. This plot, yields anactivation energy of 540 kJ/mol, in fair agreement with the literaturevalues of 475-550 kJ/mol. In our experiment, higher values of n,commonly found in superplastic deformation of zirconia, yield activationenergy numbers that are too high to be compatible with the literaturedata. For example, a value of n=2 would produce an activation energy of980 kJ/mol. Furthermore, n=1 is the ideal value predicted from modelsfor diffusional creep. These results suggest that neither the Arrheniusterm, nor the stress dependence were affected by the electrical field.The inference is that the electrical field has an influence on thepre-exponential, D₀. This point is further addressed in discussion.

(6) Microstructure and Sintered Density

The density of the samples was measured after completion of theexperiment using the Archimedes method, with de-ionized water as thebuoyant medium All samples reached a density that was 95%-98% of thetheoretical maximum. The samples for the grain size measurement wereprepared by polishing with silicon carbide paper and diamond paste downto 1 μm. After polishing, the samples were thermally etched at 1100° C.for 30 min, and then coated with a 0.5 nm film of Au—Pd, and examined ina scanning electron microscope. A typical micrograph is given in FIG.39. It shows equiaxed grain morphology with some large pores. It isthese large pores, which arise from imperfect packing of the particlesin the green state which appear to be responsible for the slight shortfall in the full density of the specimens.

The grain size in the sintered specimens was determined by measuring theaverage linear intercept and multiplying that number by 1.56. Theaverage grain size in all specimens was 135±15 nm.

IV. Discussion

(1) Summary of Results

The applied electric field and a threshold temperature characterized thephenomenon of flash sintering. This temperature falls as the appliedfield is increased.

In the present work, the additional role of a uniaxial applied stress onflash sintering has been studied. The three principal results from thiswork were as follows:

The applied stress acts like the electric field in its effect on thethreshold temperature: the critical temperature for flash sintering waslowered as the applied stress was increased.

Flash sintering was accompanied by a power surge resulting in Jouleheating of the specimen. Measurements show that the specimen temperaturerose to ˜1100° C., about 200° C. above the furnace temperature, which isstill far too low to explain sintering in just a few seconds.

In addition to sintering, field assisted superplasticity was alsoobserved. The superplastic strain increased with applied stress when theexperiments were carried out at a constant field. However, the shearstrain remained constant when the applied field was increased while theapplied stress was held constant.

Shear deformation, or superplasticity, was driven by shear stress.Therefore, it was to be expected that the shear strain would increase asthe applied stress was increased. What is noteworthy is that themagnitude of the shear strain remains constant when different electricalfields are applied at a constant applied stress. The effect of the fieldwas to enable superplastic deformation at lower temperatures. Uponconsulting Eq. (5), which is a product of the stress-dependent term, anda kinetic term, we infer that electric field influences thetemperature-dependent kinetic term in the equation.

The kinetic term is a product of a pre-exponential, D₀, and theArrhenius term, exp(−Q/RT). The discussion pertaining to Eq. (7) andFIG. 38 suggests that the electric field does not influence theactivation energy. The data (the finding of constant shear strain atdifferent applied fields) suggest that D₀ exp(−Q/RT) remained constantdespite a drop in temperature as the applied field was increased. It canthen be argued that a lowering of temperature, which reduced the exp(−Q/RT) term, must be compensated by an increase in D0 as the field wasincreased, since the product of these two terms remained unchanged.Thus, an analysis of the superplasticity data suggest that it is thispre-exponential factor of the diffusion coefficient that issignificantly enhanced by the electrical field.

More broadly, the exposition of the underlying atomistic mechanism forflash sintering needs to take stock of two important findings from thecurrent work: (i) the applied stress had the same effect on the processas the electrical field: both served to reduce the temperature for theonset of the flash event, and (ii) while flash sintering was accompaniedby an abrupt increase in the electronic conductivity of the specimen,the Joule heating produced by the accompanying increase in powerdissipation did not produce a high enough temperature to explainsintering in just a few seconds. Instead, it was necessary to discover amechanism that can simultaneously increase the conductivity and thesintering rate.

(2) Discussion of a Mechanism

The two issues stated just above are addressed in sequence. The couplingbetween applied stress and the electrical field is explained on thebasis of experiments on electro-chemomechanical potential by Pannikkatand Raj. They showed that a normal traction applied to a surface inzirconia generates an electrical potential relative to the surface thatis stress free. The reason is that the much higher mobility of oxygenions (relative to cations) means that the electrochemical potential ofthese anions must be equal at both the loaded and the stress freeinterfaces. Since the applied traction changes the chemical potential ofthese ions at the stressed interface, an electrical potential developsthat is equal and opposite to this chemical potential. The potentialdifference that develops between these two interfaces is then given by:

$\begin{matrix}{{\Delta \; \varphi} = \frac{\sigma_{e}\Omega_{O^{2 -}}}{2e}} & (8)\end{matrix}$

where Δφ is the potential difference in volts, Ω_(O) ²⁻ is the volume ofthe oxygen ion, and e is the charge of an electron in Coulombs. Thefactor of 2 in the denominator reflects the charge number for oxygenions. Following Pannikkat and Raj, we assign, Ω_(O) ²⁻=0:00884 nm³ andset e=1.60×10⁻¹⁹ Coulombs to obtain a value for Δφ as a function of theapplied stress, σ_(e).

The expression in Eq. (8) applies not only to external surfaces but alsoto internal interfaces where the oxygen ions are mobile. Thus, adifference in the normal traction at the interfaces surrounding a singlegrain, which after all is the fundamental basis of the models fordiffusional creep, would also give rise to Δφ across the grains,creating internal electrical fields that are approximately given by:

$\begin{matrix}{{\Delta \; E} = \frac{\Delta \; \varphi}{d}} & (9)\end{matrix}$

Therefore, the total electrical field experienced within the grains,E_(s), will be equal, on the average, to the sum of the applied field,E*, and the internal field given by Eq. (9):

E _(s) =E*+ΔE  (10)

Combining Eqs. (8), (9), and (10), we obtain that:

$\begin{matrix}{E_{s} = {E^{*} + \frac{\sigma_{e}\Omega_{O^{2 -}}}{2{ed}}}} & (11)\end{matrix}$

Equation (11) provides a mechanism for coupling the stress and theelectrical field to each other in field assisted sintering. In this way,the experiments on free sintering with electrical fields can be combinedwith the present experiments where stress is an additional variable. Thedata from free sintering and sinterforging results are summarized TableII and plotted in FIG. 40. The free sintering data are from M. Cologna,et al., “Flash Sintering of Nanograin Zirconia in <5 s at 850° C.,” J.Am. Ceram. Soc., 3559, 3556-9 (2010), incorporated herein by referencein its entirety, and the sinterforging data from Eq. (11) (assuming agrain size of ˜135 nm). The apparent consistency among these differentsets of data in FIG. 40 lends support to the explanation given above.

A mechanism that can explain both the power surge and the enhancedsintering is likely to be complex since sintering requires the transportof mass that is charge neutral, while electrical conductivity requiresthe transport of charged species through the electrodes that cantransmit only electrons. One such mechanism could be the nucleation ofFrenkel pairs (a vacancy and an interstitial of the same species) underan electrical field. The pair would have opposite charges on them, one ahole and the other an electron, which can be stripped by the appliedfield to leave behind charge neutral pair of a vacancy and theinterstitial. These two defects will now be able to move independentlyof one another, and migrate to the grain boundary and the pore,respectively, under the bias of the sintering pressure, to producesintering, while the electron and the hole will move through theelectrodes to feed current to the external circuit.

The Frenkel pair mechanism above is likely to be related to the localchemistry, structure, and space-charge induced electrical fields at andnear the interfaces. It seems likely that the nucleation of the defectavalanche would require a concentration of the electrical field atcharge heterogeneities within the material which amplifies the effect ofthe applied field (much like the mechanical amplification of the appliedstress at crack-tips which produces fracture at stresses that are belowthe ideal fracture stress). Grain boundary regions and the local chargeconfiguration within them could be one of these amplificationmechanisms.

V. Summary and Conclusions

Flash sintering, defined as densification of a powder compact in just afew seconds at anomalously low temperatures under the application of anelectrical field is also observed in sinterforging experiments. Theseflash events are characterized by a threshold temperature and a dcfield. A higher applied field lowers the threshold temperature.

The application of an applied uniaxial stress in sinterforging alsoaffects the threshold temperature. As the stress is increased, thetemperature for the onset of flash sintering is lowered.

The flash sintering is accompanied by anomalously high rates ofsuperplastic deformation under the applied deviatoric stress. Rates ashigh as 0.09 s⁻¹ at 850° C. have been achieved with an applied stress of12 MPa.

The grain size of the specimens appears to remain unaffected by theapplied field: it is ˜135 nm. This result distinguishes flash sinteringfrom the moderate influence of electrical field on the sintering rate,which, in yttria-stabilized zirconia has been shown to be related to areduction in grain growth under an electrical field.1

The applied fields do not appear to affect either the stress or thetemperature dependence for superplastic deformation, as predicted byclassical models. Instead, it is argued that the electrical fieldaffects the pre-exponential in the diffusion coefficient. Thepre-exponential is proportional to the defect concentration.

It is proposed that the flash events, induced by the electrical fieldsmay be related to the nucleation of defect avalanches that produce avast increase in the preexponential term for the diffusion coefficient.

It is suggested that the applied stress and the electrical fields cancouple together by the superimposition of the electrical fieldsgenerated within the polycrystal by the applied stress, and theexternally applied electrical fields. In this way, both serve to lowerthe threshold temperature.

Example 5 Proposed Mechanisms of Flashsintering

Flash-sintering is invariably accompanied by a highly non-linear rise inthe specimen's conductivity. Thus the specimen temperature rises abovethe furnace temperature. It is shown, below, that flash-sintering is atransient phenomenon, where the power dissipation rises quickly atfirst, but then declines towards a steady state, as the power supplyswitches from voltage to current control. The area under the powerspike, which is equal to the Joules expended in the sample during thetransient, is absorbed by the heat capacity of the specimen. Therefore,the specimen temperature rises gradually towards this steady statethrough the transient. Whereas the power spike can exceed a peak valueof 1000 mW mm⁻³, the dissipation during the current controlled regime isin the 100-400 mW mm⁻³ range. The extrapolation of sintering time from afew hours, as in conventional sintering, to a few seconds, using theactivation energy for diffusion, predicts sample temperatures that arefar in excess of the measured specimen temperature during flashsintering.

1. Introduction

In flash-sintering a powder preform sinters abruptly above a thresholdcondition. This transition is prescribed by a combination of thefurnace-temperature and the DC electrical field applied directly to thespecimen by a pair of electrodes. This phenomenon occurs in severaloxide systems, including yttria stabilized zirconia, magnesia dopedalumina, strontium titanate, cobalt manganese oxide, titania andmagnesium-aluminate spinel. A characteristic feature of this process isthat the sudden onset of sintering is accompanied by an equally abruptincrease in the conductivity of the specimen. Immediately the powersupply must be switched to current control so as to prevent electricalrunaway. In current control the power expended in the specimen declinessince the resistance of the specimen continues to fall. The specimentemperature rises gradually through the power-spike towards aquasi-steady state value in this current controlled regime.

The extent of the rise in the specimen temperature is an important firststep towards understanding the mechanism of flash-sintering. Highertemperature implies higher diffusion rate of mass transport. Thetemperature required to sinter in a just a few seconds can beextrapolated from the conventional time and temperature through theactivation energy for diffusion. The question is whether or not thespecimen temperature reaches this extrapolated value as a result ofJoule heating.

There have been at least two attempts to estimate the specimentemperature as a function of power dissipation. In one instance, thespecimen temperature was obtained by measuring the thermal expansion asa function of power input. In the other case the temperature wasestimated by a numerical simulation. It is important to note that inboth cases, power was applied to the specimen at a constant rate until asteady state was reached.

The temperature of the specimen during transient power, as in flashsintering, has also been measured, and is much lower than would beestimated assuming the peak power to be applied to the specimen at aconstant rate.

The following sections are divided into three major parts: (a) Jouleheating for steady state power dissipation, (b) the transient case offlash sintering, and (c) estimate of the specimen temperature that wouldbe required to sinter yttria stabilized zirconia in just a few seconds,which is then compared to the specimen temperature discussed in theprevious sections.

The flash-sintering experiments can be divided into two categories:sinterforging where a field as well as a uniaxial stress is applied tothe specimen, and free, two electrode experiments where the electricalfield is applied to the ends of an otherwise unconstrained specimen.

The experiments that are discussed below were carried out onyttria-doped zirconia: 3YSZ and 8YSZ.

2. Case I: Steady State Power Dissipation

This section is divided into three subsections. In the first, a modelfor Joule heating based upon black body radiation is described. Theseresults are presented in the form of maps that allow a quick estimate ofthe specimen temperature from the knowledge of the furnace temperature,the steady-state power dissipation, and the surface to volume ratio ofthe specimen. In the next two sections experimental5 and numericalsimulation6 data are compared with the black body radiation model.

2.1. Black Body Radiation Model for Joule Heating

If a sample initially at the furnace temperature, T₀, is heatedelectrically then the rise in its temperature, to T, relative to T₀, canbe estimated by assuming that the difference in the black body radiationat T and T₀ is equal to the heat dissipated within the sample. Thisapproach assumes that convection and conduction losses into theenvironment are negligible. Black body radiation increases as T⁴,therefore it is greater than the convection losses above about 800° C.(at dull red color). The conduction losses, however, depend greatly onthe electrode and system configuration and, therefore, cannot beestimated generally.

The estimate for T was analyzed in an earlier paper for small rise inthe sample temperature. It is derived in Yang D, et al. Enhancedsintering rate of zirconia (3Y-TZP) through the effect of a weak dcelectric field on grain growth. J Am Ceram Soc 2010; 93(10):2935-7,incorporated herein by reference in its entirety, which expressed inincremental form becomes:

$\begin{matrix}{\frac{\delta \; T}{T} = \frac{\delta \; W}{4A\; \sigma \; T^{4}}} & (1)\end{matrix}$

Integrating Eq. (1) between the limits of 0 to W, as sample temperaturerises from T₀ to T, leads to the following equation:

$\begin{matrix}{T = \left\lbrack {T_{0}^{4} + \frac{W}{A\; \sigma}} \right\rbrack^{1/4}} & (2)\end{matrix}$

In Eq. (2), σ=5.67×10⁻⁸ W m² K⁻⁴ is a universal physical constant, A isthe surface area of the sample in m², W is the electrical energydissipated in the sample in W, and the temperature is expressed in K.Eq. (2) assumes the emissivity of the ceramic to be unity; indeed formost oxides its value is greater than 0.9. Later, the discrepancybetween theory and experiment is tied to this assumption: a trueemissivity that is less than one would give higher specimen temperaturesthan calculated here.

The surface area of the sample, A, depends on the sample geometry. It isuseful to normalize W with respect to the volume of the sample, writtenhere as V, so that:

$\begin{matrix}{W_{V} = \frac{W}{V}} & (3)\end{matrix}$

where W_(v) is in units of Wm⁻³.

Eq. (2) can now be rewritten in normalized form as follows:

$\begin{matrix}{\frac{T}{T_{0}} = \left\lbrack {1 + {\frac{W_{V}}{\sigma \; T_{0}^{4}}\left( \frac{V}{A} \right)}} \right\rbrack^{1/4}} & (4)\end{matrix}$

Note that V/A is the volume to surface ratio, with units of m.

It can be more convenient to write W_(v) in units of mW mm⁻³, and V/A inunits of mm, in which case Eq. (4) becomes:

$\begin{matrix}\left\{ {\frac{T}{T_{0}} = {\alpha \left\lbrack {1 + {\frac{1000{W_{V}\left( {{mW}\mspace{14mu} {mm}^{- 3}} \right)}}{\sigma \; T_{0}^{4}}\left( {\frac{V}{A}({mm})} \right)}} \right\rbrack}^{1/4}} \right\} & (5)\end{matrix}$

where the units for the key parameters are shown in brackets. α is acorrection factor to account for the fact that the emissivity of thesample is less than unity; therefore α≧1, with α being greater than oneif the emissivity is less than unity. The predictions from Eq. (5) aremapped in FIG. 41, with the assumption that α=1. The power dissipationand the furnace temperature are the axes. Knowing these two parameters,the estimate of the specimen temperature can be read quickly. Since theresults depend on the volume to surface area ratio, four maps for(V/A)=0.5, 0.75, 1.0, and 2.0 mm are given. For example, if the furnacetemperature is 1100° C., then in order to reach a specimen temperatureof 1450° C., a power density of 600 mW mm⁻³ would be required for(V/A)=0.5 mm, or 150 mW mm⁻³ if (V/A)=2.0 mm, and so on. The predictionsfrom Eq. (5) are compared to experiments and a numerical simulation inthe next section.

In the following sections we shall find that Eq. (5) underestimates thespecimen temperature by 100-200° C., most likely because the oxide hasan emissivity that is less than unity.

2.2. Comparison with Numerical Simulation6

Soon after the publication of flash-sintering in 3YSZ zirconia, theexperiment was repeated as described in Grasso S, et al., Modeling ofthe temperature distribution of flash sintered zirconia. J Ceram Soc Jpn2011; 119(2):144-6, incorporated herein by reference. Grasso et al.sought to explain the phenomenon in terms of Joule heating by numericalsimulation. Their specimen geometry was approximately the same as inCologna M, et al., Flash sintering of nanograin zirconia in <5 s at 850°C. J Am Ceram Soc 2010; 93(11):3557-9, incorporated herein by reference,that is a rectangular gage section, 21 mm long with a cross section of 3mm×1.58 mm, which gives (V/A)=0.52 mm. In the simulation they assumed a(steady state) power dissipation of 70 W which corresponds to 700 mWmm⁻³, and a furnace temperature of T₀=850° C. The reading from FIG. 41,marked as point (A), predicts a specimen temperature of 1400° C. Thesimulation gave a range of temperatures in the specimen, with thehighest value reaching 1600° C. The underestimate is attributed to theemissivity of the specimen being less than unity.

2.3. Comparison with Experimental Results5

In Baraki R, et al., Effect of electrical field/current on sintering offully stabilized zirconia. J Am Ceram Soc 2012; 95(1):75-8, incorporatedherein by reference in its entirety, the temperature of a 95% densesample of 8YSZ were measured as a function of the power dissipated inthe specimen. The sample was a cylindrical piece, 8 mm in diameter and 4mm tall, which gives (V/A)=1.0 mm. The furnace temperature was, T₀=1200°C. The specimen temperature was estimated from volumetric thermalexpansion. These measurements are compared with the prediction of thefurnace temperature, from Eq. (5), in FIG. 42. In this instance, theagreement is reasonably fair with the model underestimating the specimentemperature by approximately 100° C. at a power level of 400 mW mm³, asshown by the point (B) in FIG. 41.

3. Case II: Flash-Sintering, the Transient Case

In this section we discuss Joule heating during a flashsinteringexperiment. Experiments have been carried out by first applying aconstant dc electric field to the specimen, and then ramping the furnacetemperature at a rate of 10° C. min⁻¹. The current in the specimen roseabruptly at a threshold value of the temperature. The power supply wasquickly switched from voltage control to current control upon reaching apreset value of the current. The power to the specimen then fell sharplysince its conductivity continues to increase, before settling down to aquasi-steady state level. The power-vs.-time curve, therefore showed aspike with an effective width of about 1 s. The question that isaddressed in the following sections is how the power dissipation isrelated to the specimen temperature, in the time domain.

This section is divided into two sub-sections. The first considers flashsinterforging of cylindrical specimens under a uniaxial load. The secondconsiders flash sintering of unconstrained dogbone shaped specimens.

3.1. Flash Sinterforging of 3YSZ

A typical set of results from a sinterforging experiment is given inFIG. 43. In this experiment a load of 5 MPa and a field equal to 100 Vcm⁻¹ were applied. The furnace was then heated at a constant rate of 10°C. min⁻¹. The onset of flash sintering took place when the furnacetemperature was approximately 875° C. The samples were of a cylindricalshape with a diameter of 5 mm and 10 mm long, giving a value (V/A)=0.75mm (considering only the bare surface of the cylinder).

The temperature of the specimen was measured by focusing a pyrometer onits surface. The pyrometer had been previously calibrated with a dense3YSZ sample placed within a furnace (without applying electrical field)and then raising the furnace temperature in steps up to 1400° C.

The upper graph in FIG. 43 shows the power density, and the specimentemperature. It spans a range from 800° C. to 900° C. Note that thefurnace temperature and the pyrometer temperature agree perfectly untilthe onset of the power surge, when the specimen temperature begins tooutpace the furnace temperature. Upon reaching a power density of 450 mWmm⁻³ the power supply was switched from voltage control to currentcontrol. The power into the specimen immediately began to decline.Meanwhile the temperature of the specimen continued to increase, throughthe transient, finally approaching a steady state. At this point thepower dissipation in the specimen also approached a quasi-steady state.

An expanded view of the data spanning 870-890° C. is given in the lowerhalf of FIG. 43. The power density immediately falls after spiking at450 mW mm³, declining to 250 mW mm⁻³ in less than 2 s. Gradually, boththe power and the temperature approach a steady state such that aspecimen temperature of 1125° C. is achieved at a power density of 125mW mm⁻³. This measurement is shown as point (C) in the maps in FIG. 41.In this case, the experimental and the calculated temperatures are infair agreement.

In Section 4 we will estimate how high the temperature must rise abovethe conventional sintering temperature in order to achieve sintering injust a few seconds.

3.2. Flash Sintering Experiments without Uniaxial Load

Unconstrained flash-sintering experiments have been carried out withdog-bone shaped specimens, suspended into a conventional furnace withtwo platinum wires that also serve as the electrodes to supply electricfield and current to the specimen. The field was applied before thefurnace was ramped up at 10° C. min⁻¹. The gage section of the specimenswas 21 mm long with a rectangular cross section of 1.58 mm×3.0 mm.Explicit details of the method are given in Cologna M, et al., Fieldassisted and flash sintering of alumina and its relationship toconductivity and MgO-doping. J Eur Ceram Soc 2011; 31(11):2827-37,incorporated herein by reference in its entirety.

In all instances the power-time plot has the same shape as shown in FIG.43 for the sinterforging experiment.

A typical result from these experiments, in this instance with 3YSZ, isshown in FIG. 44. It shows the flash regime spanning a total time of 30s, during which period the furnace temperature rises from 905° C. to910° C. In this instance the current was limited to 40 mA mm⁻². Thelower graph gives the power-profile, and the upper plot shows thesintering profile. It is to be noted that the power spike is less than 1s. The steady state power dissipation, which is achieved in currentcontrol is about one half the peak value, at approximately 200 mW mm⁻³.

The DC field required to induce flash sintering varies greatly from onematerial to another. For example in the case of YSZ the range is from 30V cm⁻¹ to 120 V cm⁻¹. In MgO-doped alumina the field can be as high as1000 V cm⁻¹, while in the case of cobalt-manganese oxide it is muchsmaller, about 12.5 V cm⁻¹. Yet in all instances the peak value of thepower dissipation is nearly the same. The quasi-steady state power inthe current control regime usually approaches one half of the peakvalue, and lies in the 100-400 mW mm⁻³ range. Therefore, the currentlimit set in the experiments is highly variable. For example, while itwas 40 mA mm⁻² for 3YSZ, it was only 12 mA mm² for MgO-alumina, but morethan 2000 mA mm² for the case of cobalt manganese oxide.

4. Extrapolation from Conventional Sintering

The absolute rates of sintering in flash sintering are very fast indeed,amounting to just a few seconds. In comparison conventional sinteringneeds an hour or more to achieve full density. Thus, the sintering ratesare three to four orders of magnitude faster in flash-sintering ascompared to conventional sintering. Here, assuming that the accelerationin sintering occurs from Joule heating of the specimen, we attempt toestimate how high the temperature must be in order to achieveaccelerated sintering of this magnitude.

The Arrhenius form of the diffusion coefficient immediately leads to thefollowing equation for establishing this relationship:

$\begin{matrix}{{\log_{10}\frac{{Rate}_{2}}{{Rate}_{1}}} = {\frac{Q}{2.3R}\left( {\frac{1}{T_{1}} - \frac{1}{T_{2}}} \right)}} & (6)\end{matrix}$

where the subscript 1 refers to the temperature for conventionalsintering, and subscript 2 corresponds to the higher rate at the highertemperature. Plots of Eq. (6) for three values of the activation energy,Q=400, 500, and 600 kJ mol⁻³, are given in FIG. 45. These graphs permita quick estimate of the temperature that would be required to acceleratethe sintering rate by several orders of magnitude.

For example, assume that conventional sintering of 3YSZ requires 1 h at1450° C. We wish to estimate the temperature that would be needed tosinter in 3.6 s, that is, 1000 times faster. The graph shows that anincrease in the sintering rate by a factor of 1000 would require atemperature of 1900° C., if the activation energy is 500 kJ mol⁻¹.10

As seen from the maps in FIG. 41, a power density of 400 mW mm⁻³ at afurnace temperature of 900° C. would yield a specimen temperature of1250° C., a difference of 350° C. Even allowing that the black bodymodel underestimates the specimen temperature by 200° C., an upper boundvalue from comparisons presented earlier, the specimen temperature fallsfar short of 1900° C. that would be required from the Arrheniusextrapolation.

5. The Heat Capacity and the Width of the Power Spike

The results in FIGS. 43 and 44 show the power spike to have a width ofapproximately 1 s. Assuming a triangular shape of the spike, and thewidth at half maximum to be 1 s, the power expended in the specimenduring this transient would be equal to P^(max)w×1 mJ mm⁻³, P^(max)w isexpressed in units of mW mm⁻³. Even if the peak value is 1000 mW mm⁻³,the highest value seen in our experiments, the energy dissipated as heatin the specimen during this short period would be <1 J mm⁻³. Thequestion addressed here is what would be the increase in the specimentemperature as a result of this heat input into 3YSZ. The density ofzirconia is 5.7 g cm⁻³, and its heat capacity varies with yttria contentand the phase of zirconia, but is generally in the range 75-85 J K-1mol-1. We shall assume a value of 80 J K⁻¹ mol⁻¹ which translates into0.65 J g⁻¹ K⁻¹ for the heat capacity for the molecular weight of 123 gmol⁻¹. One mm³ of zirconia weighs 0.0057 g mm⁻³, which then gives thefollowing value for the heat capacity per unit volume: 0.004 J mm⁻³ K⁻¹.

It follows that heat dissipation of 1 J mm⁻³, with a heat capacity of0.004 J mm⁻³ K⁻¹ would give a temperature increase of 250° C. in thespecimen, which is smaller than the temperature rise predicted fromblack body radiation. The inference is that the heat-dissipated duringthe power-spike in the flash experiments will be entirely consumed bythe heat capacity of the material.

6. Conductivity as a Function of Temperature

In this section the behavior of the conductivity in the nonlinear regimeis analyzed. The results are from experiments with 8YSZ samples that hada density of 95%, achieved by conventional sintering.

The above analysis is possible because the specimen was operated undercurrent control. A step-wise application of current to the specimenleads to a spike in the voltage generated across it, but which declinesquickly to a steady state value. Since the voltage and the currentapplied to the specimen are now constant the sample is being supplied aconstant level of power and a steady state in specimen temperature isestablished.

The specimen temperature was measured at different values of the steadystate current. These data, therefore, permit the calculation of thespecific resistivity of the specimen as a function of temperature.(These experiments were done under AC currents; the values for currentdensity are the root mean square, RMS, values.)

The basic equations for the analysis are the current density, j, theelectric field, E, the power dissipation per unit volume, W_(v), and thespecific resistivity, ρ. The following units for these parameters areused:

j mA mm⁻² , E V cm ⁻¹ , W _(v) mW mm⁻³, ρ Ohm cm  (7)

They are related by the following equations:

$\begin{matrix}{{{W_{V} = {\frac{E_{j}}{10}{mW}\mspace{14mu} {mm}^{- 3}}},{\rho = {\frac{10E}{j}{Ohm}\mspace{14mu} {cm}}},{and}}{\rho = {\frac{100W_{V}}{j^{2}}{Ohm}\mspace{14mu} {cm}}}} & (8)\end{matrix}$

where the units given in Eq. (7) are applied to Eq. (8).

The author of Grasso et al., above, has kindly supplied the data for thecurrent density, and the power density, and the specific resistivity ofthe specimens as a function of temperature, which are given as Table 3.

TABLE 3 The relationship between specimen temperature (as measured bythermal expansion) and its specific resistance. Specimen Specificresistivity Electrical field Current density temperature (° C.) (Ohm cm)(V cm⁻¹) (mA mm⁻²) 1224 4.71 8.8 19 1274 3.80 13.6 36 1341 3.25 17.4 541410 2.85 20.4 72 1476 2.55 22.6 89 1549 2.31 24.2 105 1589 2.10 25.1120 1650 1.93 26.4 137

The numbers show the resistivity to decrease by just a factor of 2.5when the temperature increases from 1275° C. to 1700° C. An Arrheniusplot of these data in FIG. 46, gives an activation energy of 0.46 eV.Thus, in the “flash regime” the material behaves like a semiconductorwith a small band gap.

The conductivity of YSZ under flash conditions, as discussed above, isalmost certainly electronic, rather than ionic, for the followingreasons:

(i) The activation energy for the diffusion of oxygen ions in dopedzirconia ranges up to 1.2 eV. In the case of 8 mol % YSZ the activationenergy ranges from 0.8 to 1 eV. Experimentally, the activation energyhas been found to increase with increasing yttria content. However, theactivation energy declines with increasing temperature which isattributed to the aggregation of defects. Since the experiments foroxygen ion diffusion are usually conducted in the 300-1000° C. range,one can question how low the value of the activation energy may be atmuch higher temperatures. But the activation energy cannot be lower thanthe value for hopping energy for oxygen ions, which has been calculatedto be 0.63 eV, still higher than the measured value of 0.46 eV.

(ii) High current of oxygen ions through the specimen would lead toreduction of zirconium oxide at the cathode into zirconium metal, whichwe do not find.

(iii) We have observed that the anode where oxygen ions oxidize intooxygen heats up due to the high electrode-interface resistance arisingfrom the release of oxygen. However, upon entering the flash regime, theelectrode immediately cools, which is explained by a transition toelectronic conduction which renders the metal-electrodes to becomenon-blocking.

7. Discussion

The phenomenon of flash sintering has an important characteristic: theonset of rapid sintering is accompanied by a highly non-linear increasein the conductivity of the specimen. The dichotomy in understanding theunderlying mechanism arises from the difference in the fundamentalnature of electrical conductivity, which is controlled by the fastestmoving charged species, and sintering, where mass transport iscontrolled by slowest moving charged species.

This dichotomy may be resolved by Joule heating. The argument being thatthe rise in temperature arising from Joule heating, produced by thesudden increase in electrical conductivity, increases the rate ofchemical diffusion. If the power density exceeds 1000 mW mm⁻³ then it isconceivable that specimen temperatures of up to 1800° C. can be reachedwhich could be high enough to explain the sintering of YSZ specimens injust a few seconds.

However, the flash sintering experiments do not endure such high powerdensities in a sustained way. While the peak value of the power-spikecan be high, the steady state power density, once the spike has passed,is far lower. The spike occurs because the power supply is switched fromvoltage control to current control to avoid electrical runaway. Undercurrent control the power declines as the resistance of the specimencontinues to fall. The steady state power dissipation regime isapproximately 125-200 mW mm⁻³. These levels of power dissipation areunlikely to produce temperatures that would be required to achievesintering in a few seconds.

What then may be the mechanism for explaining flashsintering? The onsetof the flash phenomenon is related not only to the temperature but alsoto the electrical field. In the flash regime the specimens becomeelectronically conducting. The production of Frenkel pairs and theirionization under the electric field has been proposed to explain theincrease both the electrical conductivity and the mass transport.

There remains the question to what extent Joule heating contributes toflash-sintering. The specimen temperature, though several degrees higherthan the furnace temperature, remains well below the temperature thatwould be required to densify in just a few seconds. Therefore, we inferthat sintering kinetics is enhanced by the production of defects, asdiscussed just above. The important question to ask is how Joule heatingcontributes to the mechanism of defect production.

It is interesting to note that in oxides of different chemistries, ionicand electronic conductivities, and stoichiometry, the power dissipationin the flash-regime usually falls in the 100-400 mW mm⁻³ range, eventhough the threshold values of field and temperature, for theflash-transition, vary greatly. This observation raises the question iflocal heating at grain boundaries is precipitating the instability; thisexplanation can be explored by studying the influence of the grain size,even extending to single crystals, on the flash-transition.

Recent works on “flash welding” of YSZ powders shows effects similar tothose seen in flash sintering. There is a large increase in conductivityabove a threshold applied field, and the resistance of the specimendeclines thereafter. The authors attributed these observations to Jouleheating.

The influence of an electric field on the tensile superplasticdeformation of oxides has been studied before. Significant drops werereported in the flow stress, which were partitioned into threecomponents: the first arising from Joule heating, the second beinglinked to the immediate influence of the field on transport kineticssince the flow stress is seen to fall and rise as the field is turned onand off, and the third being related to the cumulative influence of theapplied field on the microstructure—principally grain growth—during theexperiment. The large effect seen in the on-off experiments withMgO-doped alumina are particularly noteworthy. In view of the very highfurnace temperatures in these experiments it is possible that thesamples were being operated in the high conductivity regime (while thefields used in the deformation experiments were lower than those inflash sintering of MgOAl₂O₃, the furnace temperatures were much higher;the critical field for the flash event declines as the furnacetemperature rises). Measurements of the power density would serve toclarify this point.

8. Conclusions

Flash sintering of several oxides is invariably accompanied by a suddenincrease in the conductivity of the specimen. This observation requiresa mechanism that can explain a simultaneous increase in electricalconductivity and mass transport kinetics. However, the first iscontrolled by the fastest moving, and the latter by the slowest movingcharged species.

Joule heating of the specimen is a simple way to explain this couplingbetween charge and mass transport. The transient nature of theflash-sintering process, however, requires care in estimating thespecimen temperature. The increase in conductivity produces a surge inpower dissipation when a constant voltage is applied to the specimen.The power supply switches to current control when the power reaches apreset value, which causes the power dissipation to decline and finallyapproach a steady state. The analysis of this power spike shows thatspecimen temperature is determined not by the peak value of the spike,but by the steady state value of the power dissipation in the currentcontrolled regime. The measurement of specimen temperature agrees withthese estimated values.

While the specimen temperature rises a few hundred degrees above thefurnace temperature, it remains several hundred degrees below thetemperature that would be required to sinter the specimen in a fewseconds.

Therefore, Joule heating, by itself, cannot explain the phenomenon offlash-sintering. It is proposed that the applied field and the higherspecimen temperature act synergistically to produce an avalanche ofdefects, such as Frenkel pairs, that greatly enhance the rate of masstransport.

Example 6 Particle Sizing Effects

The study of 3 mol % yttria stabilized zirconia (3YSZ) with differentparticle sizes provides new insights into flash sintering. Four powders,all with the same crystallite size but various particle size wereinvestigated: described as nominally 1 μm (D80=0.51 μm, meaning 80 vol %has a size less than 0.51 μm), 2 μm (D80=0.90 μm), 5 μm (D80=2.11 μm)and 10 μm (D80=3.09 μm). While the furnace temperature for flashsintering, at a field of 100 V cm⁻¹, increased from 920° C. to 1040° C.with particle size, the specimen temperature in all instances remainedat ˜1200° C. The quantum increase in density decreased with largerparticles. The grain size distribution of conventionally and flashsintered specimens remained similar, with some evidence of apreponderance of nanograins in the flash sintered specimens. Jouleheating was well below the temperatures that would have been requiredfor sintering in a few seconds. An explanation based upon the nucleationof Frenkel pairs is proposed.

1. Introduction

Two electrode experiments where electrical fields were applied directlyto otherwise bare specimens were providing incontrovertible evidence forfield-assisted sintering phenomenon in oxide ceramics. When applied to 3mol %1 and 8 mol %2 yttria stabilized zirconia, these experiments haverevealed two regimes of behavior. At low fields, typically less than 40V cm⁻¹, the sintering rate increases incrementally relative toconventional sintering. This behavior has been attributed to a reductionin grain growth under an applied field.

At higher fields, typically greater than ˜60 V cm⁻¹, a new phenomenon isobserved: the YSZ specimens sinter almost instantaneously, as if in aflash, above a critical temperature. This threshold temperaturedecreases as the applied (DC) field is increased. Flash sintering hasbeen observed in MgO-doped alumina, titania, magnesium aluminate spinel,ceria, cobalt manganese oxide and strontium titanate in published andunpublished work from our laboratory. Other groups are also performingfield assisted sintering experiments showing similar results.

While the fundamental mechanism of mass transport in flashsinteringremains obscure, one feature of this phenomenon is shared by all oxides:the onset of flash sintering is accompanied by a highly non-linearincrease in the conductivity of the specimen. The increase inconductivity leads to Joule heating. A careful analysis and directmeasurements of the specimen temperature, however, preclude thepossibility that Joule heating alone can account for sintering in mereseconds. These findings urge a search for an alternative mechanism toexplain this effect. A key question is how it can be that a massiveincrease in charge neutral mass transport, as required for sintering, iscoupled to a similar increase in conductivity, which is controlled bythe fast moving charge species. Mass transport, or chemical diffusion isnominally controlled by the slowest moving charge.

The results from particle size effects reported here provide new inputsto the discovery of flash sintering. It was found that the powerdissipation at the onset of the flash remained independent of theparticle size, as did the maximum temperature of the specimens asmeasured directly with a pyrometer, even though the furnace temperaturefor the onset of sintering increased continuously with particles size. Asecond remarkable observation was that the quantum increased in densityduring the flash decreased with particle size. We propose Frenkel pairnucleation as a possible route to piecing together this interestingpuzzle.

2. Experimental

2.1. The Method

The setup for the flash-sintering experiments is described above,Briefly, the sample was suspended in the center of a vertical tubularfurnace by means of two platinum electrodes, which were also used tocarry the electrical power to the specimen. The “green” specimen had adog-bone shape with a gauge length of 2 cm, and a cross section of 1.6mm×3.3 mm. The handles of the dog-bone had holes through which theplatinum electrodes were inserted, like a hook.

The sintering experiment was conducted by applying a voltage to thespecimen at ambient temperature, and then heating the furnace at aconstant rate of 10° C. min⁻¹. In the present experiments two appliedvoltages were used, 200 V and 40 V or a field of 100 V cm⁻¹ and 20 Vcm⁻¹, respectively. The onset of sintering is accompanied by rapidincrease of the power dissipated in the specimen. Therefore, the powersupply is set to switch to current control when the current reaches apreset value. Under current control, the power dissipation, which isgiven by I2R, where I is the current and R is the resistance, begins todecline since the conductivity of the specimen continues to increase.Thus, the shape of the power cycle consists of a sharp spike undervoltage control followed by a quick decline towards a steady state undercurrent control. The sample temperature during this protocol, however,rises gradually towards a steady state, with the power spike beingabsorbed by the heat capacity of the specimen, and the maximumtemperature of the specimen being determined by the level of the steadystate power supplied to it under current control.

The sintering strain is expressed by the linear shrinkage in the gaugesection of the specimen, which is measured from pictures acquired with aCCD camera through an optical filter and a silica window placedunderneath the furnace.5 The shrinkage strain is calculated as the truestrain, ∈=ln(I/Io), where l is the time dependent gauge-length and l_(o)is the initial gauge length. The camera is set to record photographs atone-third of a second to one-second intervals.

2.2. Materials

The starting powder for the sintering experiments was tetragonalzirconia doped with 3 mol % yttria (3YSZ), supplied by UCM AdvancedMaterials GmBH, Germany. Four different particles sized were used,denoted nominally as 1 μm, 2 μm, 5 μm and 10 μm, as per manufacturer'sspecification. The powder size distributions in terms of D80, D50 andD₂₀ are reported in Table 4.

TABLE 4 Powder size distribution of the UCM zirconia powders (fromsupplier's certificate of analysis). Powder size D80 D50 D20(manufacturer designation) (μm) (μm) (μm)  1 μm 0.51 0.33 0.21  2 μm0.9  0.56 0.35  5 μm 2.11 1.16 0.65 10 μm 3.08 1.69 0.85

These numbers specify the volume fraction of the particles lying belowthe D-value. For example, D50=1.16 μm for the particle size group of 5μm means that 50% of the particles in that group, by volume, have a sizethat is smaller than 1.16 μm. Alternatively, the D80=3.08 μm andD50=1.69 μm for the group of 10 μm means that the difference, that is,30% of the particles in this group lie in the range 3.08-1.69 μm.

To prepare the dog-bone shaped specimens the powders were mixed with 5wt % polyvinyl alcohol (mol. wt. 49,000) in water. The slurry was driedat 90° C. in an oven and ground to a powder in mortar and pestle. Theresulting powders were uniaxially pressed at 280 MPa in a dog boneshaped die, to a green density of 55%, 57%, 58% and 59%±1%, for the 1,2, 5 and 10 μm powders. The dimensions of the cross section of the gagewere 1.6 mm×3.3 mm, while the gauge length was 2 cm.

The grain size was measured from images taken with a JSM-7401F fieldemission SEM (JEOL). Specimens were prepared by polishing to 1 μm,thermal etching for 30 min at 1100° C., followed by coating with a witha 2 nm layer of Au—Pd. The mean grain size was determined by the linearintercept method, with a correction factor of 1.56.

3. Results

3.1. Conventional Sintering

Without the electric field, the samples sintered slowly as thetemperature of the furnace was raised. The results are shown graphicallyin FIG. 47, and summarized in Table 5.

TABLE 5 Results from conventional sintering (0 V). Constant heating rate10° C. min⁻¹ Temperature range: ambient to 1450° C. Powder size FinalLinear shrinkage Maximum rate (manufacturer designation) density strainof sintering  1 μm 96% 0.182 0.00013 s⁻¹  2 μm 84% 0.130  5 μm 72% 0.07110 μm 68% 0.046

The samples with the smallest particle size began to sinter at thelowest temperature, approximately 1100° C., and reached the highestdensity when the furnace reached 1450° C., at which point the experimentwas stopped. As the particle size increased the onset of sintering wasdelayed, and the final density at 1450° C. was consistently lower. Thefinal shrinkage strain was −0.182, −0.130, −0.071 and −0.046, for the 1,2, 5 and 10 μm powders. The sintered density, ρ, is related to the greendensity, ρg, through the true linear shrinkage strain, ∈linear, by thefollowing equation13:

$\begin{matrix}{{3{ɛ_{linear}}} = {\ln \left( \frac{\rho}{\rho_{g}} \right)}} & (1)\end{matrix}$

Substituting the values for ∈_(linear) given just above, and for thegreen density quoted earlier, the final density of the samples sinteredwithout the electric field was 95%, 84%, 72% and 68% for the 1, 2, 5 and10 μm powders. Among these only the 1 μm specimen was suitable formechanical polishing to obtain SEM micrographs of the grain size.

3.2. Flash Sintering

Flash sintering was observed in all experiments. The shrinkage strainversus temperature data for different particle sizes at an applied fieldof 100 V cm⁻¹, all obtained at a constant heating rate of 10° C. min⁻¹,are shown in FIG. 47. The results are summarized in Table 6.

TABLE 6 Results from flash sintering (100 V cm⁻¹) Constant heating rate10° C. min⁻¹ DC field = 100 V cm⁻¹ Maxi- Flash Maxi- Linear Maxi- mumtemper- mum shrink- mum rate of Green ature specimen Final age rate ofsintering density (furnace) temperature density strain sintering  1 μm55%  920° C. 1150 ± 25° C. 96% 0.186 0.048 s⁻¹  2 μm 57%  955° C. 1175 ±25° C. 84% 0.129 0.028 s⁻¹  5 μm 58%  990° C. 1125 ± 25° C. 82% 0.1150.017 s⁻¹ 10 μm 59% 1040° C. 1200 ± 25° C. 82% 0.110 0.017 s⁻¹

The temperature for the onset of flash sintering depends on the particlesize, being at 920° C., 955° C., 990° C. and 1040° C. for the 1, 2, 5and 10 μm powders. The final density decreases with particle size. Usingthe data in FIG. 47 and applying Eq. (1) the final density is calculatedto be 96%, 84%, 82% and 82% for the 1, 2, 5 and 10 μm powders.

Since the overall duration of the flash sintering event lasts about 5 s,and since the images of the sample are taken every one second, it ispossible to calculate the shrinkage rates during the flash sinteringprocess. These results are given in FIG. 48. They reach a maximum of4.8% s⁻¹ for the 1 μm sample, 2.8% s⁻¹ for the 2 μm sample, and 1.7% s⁻¹for the 5 μm and 10 μm samples. Therefore, large particles do not have asignificant effect on the rate of sintering, but instead they limit thefinal density that can be achieved during the flash process.

Comparing the data for 1 μm sample in Tables 2 and 3 shows that thesintering rate with the applied field was nearly 350 times faster ascompared to conventional sintering. This difference is all the moreremarkable because the furnace temperature for flash sintering was muchlower than in conventional sintering.

3.3. Field Enhanced Sintering

Field enhanced sintering is characterized by a faster rate of sintering,relative to conventional sintering, without changing the overallcharacter of the sintering curves. Such behavior has been seen in 3YSZat applied fields that are below the threshold for flash sintering.1 Inthe present set of experiments this behavior is seen in the 1 μmspecimen, and to a lesser degree in the 2 μm sample, but not for thespecimens of larger particle size. The results for 0 V and 20 V cm⁻¹experiments are given in FIG. 49.

In earlier work such enhancement in the sintering of 3YSZ has beensuccessfully explained by the influence of the electrical field on graingrowth: electric field lowers the rate of grain growth, and sincesintering rate is highly sensitive to the grain size, the sintering rateis enhanced. However, the application of this concept requires that theparticle size must also be the grain size of the starting powders. Ifthe particles are large, and themselves polycrystals of small grains, aswas the case here, then this idea is invalid since the diffusiondistance which controls the sintering rate is determined not by thegrain size but by the size of the particles, which is of courseunaffected by the electric field. This explanation is offered for theabsence of enhancement in the large particle size specimens.

3.4. Joule Heating

A sudden increase in the conductivity of the specimen is an indeliblesignature of flash-sintering. The experimental results shown in FIG. 50are no exception to this rule.

Under voltage control, where the power flowing to the specimen is givenby V2/R where V is the voltage and R is the resistance, the powerdissipation continues to increase as the resistance falls.Experimentally this power surge is handled by the power supply switchingto current control when the current rises to a preset limit Now thepower dissipation is given by I2R; the power dissipation begins todecline as the resistance continues to fall. Eventually a quasisteady-state is approached, which leads to a steady temperature in thespecimen. The sample temperature does not show the power spike, sincethe energy expended in the spike is absorbed by the heat capacity of thespecimen. As a result the sample temperature rises continuously towardsa quasi-steady state.

The plots for the power density and the synchronous rise in the specimentemperature (measured with a pyrometer calibrated with a dense specimenof 3YSZ placed in the furnace) are given in FIG. 51. In each case thepower rises to a peak under voltage control and then declines as thesupply switches to current control. The specimen essentially follows thefurnace temperature until the flash event when it rises quickly towardsa quasi-steady state value.

Three features of the data in FIG. 51 are noteworthy: (i) Although thepeak height of the power spike changes (decreases) with particle size,the steady state value remains the same at ˜40 mW mm⁻³, (ii) Themagnitude of power dissipation at the cusp, at the onset of the flash,remains the same at approximately ˜10 mW mm⁻³ for all cases, and (iii)The highest value of the specimen temperature in all instances fallswithin a narrow band, as highlighted by the shaded area: it is in the1100-1200° C. range.

The above values for power dissipation and the specimen temperature inthe quasi-steady state regime are consistent with an analytical modelbased upon black body radiation.

The question arises why it is that the (furnace) flash temperatureincreases systematically from 920° C. to 1040° C. with increase in theparticle size, even though the specimen temperature achieved during theflash event is about the same. The answer apparently lies in theincrease in the resistance of the powder compacts with particle size;this can be seen from the slope of the curves below the flash in FIG.51, and also in the shifts of the curves in the logarithmic plots givenin FIG. 50.

Taken as whole the above observations strongly suggest that Jouleheating must produce a certain critical temperature in the specimen toprecipitate the flash event. Since the specimen temperature is relatedto the power dissipation, it follows that that too must reach the samevalue, regardless of the intrinsic resistance of the specimen in thedormant state. Since the large-particle compacts have a higherresistance they must be heated to a higher temperature to reach the samelevel of dissipation as the small-particle compacts, which raises theflash temperature for the larger particles. However, the maximumspecimen temperature achieved by Joule heating remains well below thetemperature that would be required to sinter the specimen in a fewseconds. This point is shown graphically in FIG. 52. It gives therelationship between time and temperature for a thermally activatedprocess. In 3YSZ the activation energy for chemical diffusion is ˜500 kJmol⁻¹. If sintering occurs in 1 h at temperature T1=1450° C., then forsintering to occur 1000 times faster, that is in 3.6 s, a temperatureT2=1900° C. would be required. This temperature is far higher than themaximum temperature of the specimens, as reported in FIG. 51.

3.5. Microstructure

The samples from larger particle size, being of low density, weredifficult to polish and prepare for microstructural characterization.Therefore results for the 1 μm sample, which sintered to 96% density aregiven.

The micrographs from a conventionally sintered and a flash sinteredsample are compared in FIG. 53. Histograms of the grain sizedistributions are included. Both microstructures are nearly identical,except for one observation. The flash-sintered sample shows clusters ofultrafine nanocrystals in pockets which are spaced apart by a distancethat rhymes with the particle size in the powder. This is also evidentin the histograms where grains less than 100 nm are more heavilypopulated in the flash-sintering specimen (for comparison this bar isshown in solid color). One possible explanation is that the rush of massinto the pores during flash sintering nucleates new grains. Inconventional sintering the process is slow enough that the matter beingdeposited on the pore surfaces can be grafted on to the crystalsurfaces. In flash sintering nearly 50% of the mass in the specimen mustbe moved to fill the pores in just a few seconds, which may be too fastfor the existing surfaces of the pores to grow as crystals with theinflow of mass, forcing the inflow to form its own grains. In a relatedobservation, small bumps were found to develop on pore surfaces underthe influence of an electric field (FIG. 53).

4. Discussion

The results presented above have the following salient features:

(i) The shift in the flash (furnace) temperature with particle sizeresults from the higher resistance of the samples with the largerparticle size. The samples for all four particle sizes reach the samespecimen temperature during Joule heating. It is the value of thisspecimen temperature, which is in the 1100° C. to 1200° C. range thatappears to be important.

(ii) The magnitude of the shrinkage strain during the flash event dropswith larger particle size. Only the 1 μm specimen reaches a density of96%, rising from a green density of 55%. The density of the specimenswith larger particle sizes, which had similar green density, increasedonly to 82-84% of theoretical.

(iii) Joule heating of the specimens cannot, in of itself explain theflash event. The specimen temperature of ˜1200° C. remains well belowthe estimated temperature of ˜1900° C. for sintering to be completed ina few seconds.

The increase in the intrinsic resistance of the powder compacts withparticle size is not unexpected. The contact area between the particles,even from Van der Waals forces, would increase when the particles aresmaller, leading to higher conductivity. For the moment, this may be asufficient explanation for the higher resistance of the compacts madefrom larger particles.

However, the massive chemical diffusion at relatively low specimentemperatures, that would be needed to transport nearly half the mass inthe specimen into the pores, remains an exciting scientific question.Joule heating seems necessary to raise the specimen temperature up to apoint, but the significance of the value of this temperature, remains amystery.

The synchronicity between the abrupt increase in electricalconductivity, and chemical diffusion poses a dilemma, since one iscontrolled by the fastest moving charge, and the other by the slowestmoving charge. Any mechanism for flash sintering must explain thiscoupling in order to be viable.

A mechanism we have suggested in the past at least conceptually isconsistent with the above observations, although the detailed expositionof it is far from clear. The mechanism calls for the nucleation ofFrenkel pairs to simultaneously provide charge and mass transport. Theconcept is that the interstitial vacancy pair can ionize under theapplied electric field liberating a hole and an electron, which provideelectrical conduction. The ionization renders the defects charge neutralrelative to the lattice, and free to migrate independent of one another.Now the migration of the vacancy to the grain boundary and theinterstitial to the pore, under the bias of the sintering pressure,effectively transports mass from the boundaries into the pore producingsintering.

The Frenkel pair mechanism is also consistent with the observation thatlarger inter-pore spacing, as with the larger particles, will increasethe probability that the vacancy and interstitials will simply recombineand become neutralized, before they can migrate to the pore and thegrain boundary, since larger particles entail longer diffusiondistances.

5. Summary

1. Four powders of 3YSZ, with particle size ranging from 1 μm to 10 μmwere successfully flash sintered, at an applied field of 100 V cm⁻¹. Thethreshold temperature for the onset of flash sintering moved higher asthe particle size increased.

2. The power dissipation in all specimens was nearly the same for allparticle sizes. As a result, the specimen temperature for all cases,produced by Joule heating, was also the same. The movement in the(furnace) flash sintering temperature can therefore be explained by thehigher electrical conductivity of the “green” samples made from thesmaller particle size.

3. The specimen temperature as measured with a pyrometer was well belowthe temperature that would have been required to achieve densificationin just a few seconds.

4. Only the specimen with the smallest particle size could be sinteredto full density. The larger particle size specimens sintered to 82-84%density.

5. A Frenkel defect nucleation mechanism is invoked to explain thesefindings. The lower density of the samples with larger particles isattributed to longer diffusion distances requiring longer times forthese defects to travel to the pores, thus competing with the lifetimesfor the recombination of the Frenkel defects.

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1. A method of sintering a material, comprising simultaneously exposingthe material to heat and to a DC, AC or pulsed electrical field that isapplied by a potential difference across the material, such that thematerial is sintered, wherein the time between the onset of sinteringand the completion of sintering is less than one minute.
 2. The methodaccording to claim 1, wherein the time between the onset of sinteringand the completion of sintering is less than 5 seconds.
 3. The methodaccording to claim 1, wherein the electrical field is between 7.5 V/cmand 1000 V/cm.
 4. The method according to claim 1, wherein the onset ofsintering is accompanied by an increase in the power dissipated withinthe material, wherein the power dissipation is manifested as an increasein the current flowing through the material.
 5. The method according toclaim 4, wherein the power dissipation of between 10 to 1000 mWmm⁻³. 6.The method according to claim 1, wherein the onset of sintering isaccompanied by a non-linear increase in the conductivity of thematerial.
 7. The method according to claim 1 wherein the electricalvoltage is applied to the material with two electrodes that areelectronically conducting.
 8. The method according to claim 1 whereinthe electrodes are made from a metal or from an electronicallyconducting ceramic material.
 9. The method according to claim 1 whereinthe electrodes are not physically in contact with the material.
 10. Themethod according to claim 1, wherein the electrical field is fixed andthe heat is increased at a constant rate until the onset of sintering.11. The method according to claim 10, wherein the heat is increased at arate between 1° C. per minute to 100° C. per minute.
 12. The methodaccording to claim 1, wherein the temperature of the furnace containingthe material is fixed and the applied voltage field is increased at aconstant rate until the onset of sintering.
 13. The method according toclaim 1, wherein the onset of sintering is accompanied by an increase inthe relative density of the material to 80-100% of the theoreticaldensity.
 14. The method according to claim 1, further comprisingsimultaneously exposing the material to an electric field and to heat,such that the material is sintered, wherein the electrical field isbetween 7.5 V/cm and 1000 V/cm, wherein the onset of sintering isaccompanied by a power dissipation between 10 to 1000 mWmm⁻³, whereinthe onset of sintering is accompanied by a non-linear increase in theconductivity of the material, and wherein the time between the onset ofsintering and the completion of sintering is less than one minute. 15.The method according to claim 1, wherein the material has a greaterconcentration of non-stoichiometric phase than Al₂O₃, wherein the Al₂O₃is substantially not doped with MgO.
 16. The method according to claim15, wherein the non-stoichiometric phases are Ruddlesden-Popper (RP)phases.
 17. The method according to claim 1, wherein the material has agreater concentration of non-stoichiometric phase than a materialselected from the group consisting of yttrium-stabilized zirconia,MgO-doped alumina, SrTiO₃ and Co₂MnO₄.
 18. The method according to claim17, wherein the non-stoichiometric phases are Ruddlesden-Popper (RP)phases.
 19. The method according to claim 1, wherein the material isselected from yttrium-stabilized zirconia, MgO-doped alumina, SrTiO₃ andCo₂MnO₄.
 20. The method according to claim 1, wherein the material isprovided in particles with average diameters between 60 nm, and 1.5 μm.21. The method according to claim 1, wherein the material is provided inparticles with average diameters between 60 nm and 200 nm.
 22. Themethod according to claim 1, wherein the material is provided inparticles with average diameters between 1.0 μm and 1.5 μm.
 23. Themethod according to claim 1, further comprising exposing the materialuniaxial force.
 24. The method according to claim 23, wherein theuniaxial force is between 1.5 and 12 MPa.
 25. A composition comprisingmaterial flash sintered according to claim 1.